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phunguyen02

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II-Thought-Math-Code-v0

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[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet $a,b,c,d,e,f,g$ be seven distinct positive integers such that\n\n\\begin{align*}\nabc &= 200\\\\\ncde&=180\\\\\nefg&=189.\n\\end{align*} What is the maximum possible value of $b+d+f$?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe 8th term of the arithmetic sequence 1, 4, 7, 10, …, is equal to ___.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n4. In the arithmetic sequence $\\left\\{a_{n}\\right\\}$, it is known that $\\left|a_{5}\\right|=\\left|a_{11}\\right|, d>0$, the positive integer $n$ that makes the sum of the first $n$ terms $S_{n}$ take the minimum value is $\\qquad$ .\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe equation $x^2 + bx + c = 0$ has roots $r$ and $s$. If $r + 2s = 12$ and $s - 3r = -7$, what is the value of $c$?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA jar contains 10 red jelly beans and 5 blue jelly beans. John chooses a jelly bean at random, writes down its color, and then puts it back. He repeats this process until he has chosen 3 red jelly beans. What is the probability that he chooses exactly 5 blue jelly beans in the process?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA group of friends want to share some identical candies among themselves. If they divide the candies into portions of equal size, and each friend must receive a portion, determine the maximum number of friends who can share the candies if the total number of portions is fixed at seven and no friend can receive more than two portions.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA 12-foot by 15-foot wall is covered with square bricks of size 1 foot by 1 foot. Each brick has a pattern consisting of a blue square of side length 1/3 foot centered at the middle of the brick. The remaining portion of the brick is painted red. How many square feet of the wall are painted red?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEmily's cake collapses and ruins 1/4 of it. She then eats 3/4 of what's left. If the original cake weighed 48 ounces, how many ounces of cake did Emily eat?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nSimplify the expression $\\sqrt{(3^3 \\div 3^2) \\cdot 2^6}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nJerry was weighing boxes for moving. The first box weighed 2 pounds, the second box weighed 11 pounds, and the last box weighed some pounds. The combined weight of all three boxes is 18 pounds. How much does the last box weigh?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe tiles of a standard 64-tile Scrabble set are arranged in a row. What is the expected number of pairs of adjacent tiles which are both vowels? Express your answer as a common fraction.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA fair coin is flipped four times. What is the probability that the number of heads is equal to the number of tails? Express your answer as a common fraction.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe sum of three consecutive odd integers is 231, and the product of the first and third integers is 245. Find the three integers.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe average age of a group of people in a meeting is 40 years. If a new person joins the group, the average age decreases by 2 years, and if another person leaves, the average age increases by 3 years. How many people are there in the meeting originally?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf $f(x)=-\\frac{1}{2}x^2+b\\ln(x+2)$ is a decreasing function on $(-1,+\\infty)$, then the range of values for $b$ is.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven the function $$f(x)= \\begin{cases} a^{x}, x<0 \\\\ ( \\frac {1}{4}-a)x+2a, x\\geq0\\end{cases}$$ such that for any $x\\_1 \\neq x\\_2$, the inequality $$\\frac {f(x_{1})-f(x_{2})}{x_{1}-x_{2}}<0$$ holds true. Determine the range of values for the real number $a$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nDr. Rodriguez is grading the mid-term exams of her students, and she needs to check 8 problems on each exam. If she has 4 sections with 28 students in each section, how many problems will she need to review in total?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nHow many different positive four-digit integers can be formed using only the digits in the set {1, 3, 3, 3, 4, 5, 5, 7} if no digit may be used more times than it appears in the given set of available digits?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the number of distinct terms in the expansion of \\((x_1 + x_2 + \\ldots + x_n)^m\\), where \\(m\\) is a positive integer greater than 1 and \\(n = 2m\\).\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n7. In the Cartesian coordinate system $x O y$, $F$ is the focus of the parabola $\\Gamma: y^{2}=2 p x(p>0)$. Point $B$ is on the $x$-axis and to the right of point $F$. Point $A$ is on $\\Gamma$, and $|A F|=$ $|B F|$. The second intersection points of lines $A F$ and $A B$ with $\\Gamma$ are $M$ and $N$, respectively. If $\\angle A M N=90^{\\circ}$, then the slope of line $A F$ is $\\qquad$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven $k$, $m$, and $n$ are integers such that $\\frac{k}{m}=\\frac{k+m}{k+n}$. If $m$ and $n$ have the same parity, determine the value of $\\frac{k+m}{m-n}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the value of $a$ such that the graph of the function $f(x) = a \\log_2(x)$ passes through the point $(16, 12)$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the sum of the series:\n\n$$\\frac{1}{1!} + \\frac{1}{2!} + \\frac{1}{3!} +... + \\frac{1}{n!}$$\n\nwhere $n$ is a positive integer. Express the sum as a simple fraction in lowest terms.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nHow many ways are there to color the cells of a $10 \\times 10$ board in blue and green such that each $2 \\times 2$ square has two blue and two green cells?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf $x + \\frac{1}{x} = 2$, then find $x^{12}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet $G(x)$ be a polynomial such that $G(2) = 5$ and\n\\[\\frac{G(x^2)}{G(x+1)} = x^2 - \\frac{x^3+3x^2-2x-1}{x^3+x^2-2x-1}\\]\nfor $x \\in \\mathbb{R}$ such that both sides are defined. Find $G(-1)$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGraeme is weighing cookies to see how many he can fit in his box. His box can only hold 40 pounds of cookies. If each cookie weighs a certain amount in ounces, and he can fit 320 cookies in the box, what is the weight of each cookie in ounces?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe altitude to the hypotenuse of a triangle with angles of 45 and 45 degrees is 2 units. What is the area of the triangle, in square units? Express your answer in simplest radical form.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThree cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a Jack, the second card is a Queen, and the third card is a King? Assuming the dealing is done without replacement.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhat is the measure, in degrees, of the acute angle formed by the second hand and the hour hand on a standard clock when it indicates 5:27?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven the polynomial $(a^2 + ka + 25) - b^2$, find a value for $k$ such that the expression can be factorized, and write the factorization process.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nCompute\n\\[\\sum_{n = 0}^\\infty \\frac{1}{x^{2^{n+1}} - x^{-2^{n+1}}}.\\]\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nAdd $21_4 + 32_4 + 332_4 + 3332_4$. Express your answer in base 4.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhat is the value of $(a@b)@(c@d)$, if $x@y = xy - 2x$ and $a, b, c, d$ are all positive integers?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet\n\\[\\mathbf{N} = \\begin{pmatrix} x & y & z \\\\ y & z & x \\\\ z & x & y \\end{pmatrix}\\]be a matrix with complex entries such that $\\mathbf{N}^3 = \\mathbf{I}.$ If $xyz = -1,$ then find the possible values of $x^4 + y^4 + z^4.$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEthan has $80 to spend on his lunch at a café. The sandwich costs $12 and the salad $8 more. The cost of the drink is 30% of the price of the salad. How much money will Ethan have left after buying all those items?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven that\n$$A=12^{1002}-12^{-1002}$$\nand\n$$B=12^{1002}+12^{-1002}$$\ndetermine $\\ds\\f{A}{B}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven a circle with center $O$ and radius $r$, points $P$ and $Q$ are chosen on the circle such that the length of arc $PQ$ is $\\frac{2\\pi r}{3}$. The chord $PQ$ divides the circle into two regions. Find the ratio of the areas of these two regions.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe terms of a geometric sequence are $a, ar, ar^2, \\ldots$. If $a>0$, what is the smallest value of $r$ such that the sum of the first 10 terms of the sequence is greater than 1000 times the sum of the first 5 terms?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven that $2 + 3\\sqrt{3}$ is a root of the equation $x^3 + px^2 + qx + 27 = 0$ and that $p$ and $q$ are rational numbers, compute $p$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWendy is a very generous kid. Every time her parents buy her some stuff, she always gives some of it to her friends. For her birthday this year, she received a new set of shoes. She gave away 14 pairs of shoes to her friends and was left with 19 pairs of shoes. How many pairs of shoes did she have in total after receiving the new set?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nMaya wants to purchase a new laptop priced at $240, but she currently has $60 saved. To afford the remaining amount, she intends to save an equal sum of money each week for three months. How much should Maya save per week?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n13. Let $x[n]$ denote $x^{x^{\\prime}}$, where there are $n$ terms of $x$. What is the minimum value of $n$ such that $9[9]<3[n]$ ?\n(For example, $3[2]=3^{3}=27 ; 2[3]=2^{2^{2}}=16$.)\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA whole number is said to be \"5-heavy\" if the remainder when the number is divided by 5 is greater than 2. What is the least three-digit 5-heavy whole number that is also a perfect square?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven a polynomial $p(x) = x^4 + \\beta x^3 + \\delta x^2 + \\epsilon x + \\zeta$, where $\\beta$, $\\delta$, $\\epsilon$, and $\\zeta$ are real numbers, determine the smallest possible value of $|\\beta| + |\\delta|$ such that $p(x)$ has exactly two distinct real roots and the sum of these roots is equal to the product of the complex roots.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA father rabbit has 10 little rabbits. The first 4 little rabbits collect 6 carrots each. Another 4 little rabbits collect 8 carrots each, and the remaining little rabbits each collect a quarter of the number of carrots that father rabbit collects. If father rabbit collects twice the total number of carrots as the first 2 groups of little rabbits, how many carrots does the family of rabbits have collectively?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nTask 11.2. Find all pairs of natural numbers $m$ and $n$ such that $m^{2019} + n$ is divisible by $m n$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf $\\mathbf{A}^{-1} = \\begin{pmatrix} 2 & 5 \\\\ -1 & -3 \\end{pmatrix},$ then find the inverse of $\\mathbf{A}^2.$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf $a^x = b^y$ and $b^z = c^x$, where $a$, $b$, and $c$ are positive integers, find the smallest possible value of $xyz$ such that $a + b + c = 20$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA fair six-sided die is rolled three times. Each roll is used as a digit in a three-digit number, with the first roll as the hundreds digit, the second roll as the tens digit, and the third roll as the units digit. What is the probability that the resulting three-digit number is divisible by 6? Express your answer as a common fraction.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven the ellipse $C$: $\\frac{x^{2}}{4} + \\frac{y^{2}}{b} = 1$ and the line $l$: $y = mx + 1$, if for any $m \\in \\mathbb{R}$, the line $l$ always intersects with the ellipse $C$, then the range of the real number $b$ is _____.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEvaluate the infinite series: $$\\frac{1}{1 \\cdot 2} + \\frac{1}{2 \\cdot 3} + \\frac{1}{3 \\cdot 4} + \\frac{1}{4 \\cdot 5} + \\dots$$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe graphs of $y = f(x)$ and $y = f^{-1}(x)$ intersect at exactly one point $(a,b).$, where $f(x) = |x+5| + 2$, Find the ordered pair $(a,b)$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nAlice has a set of 8 distinct colored balls and Bob has a set of 8 distinct colored boxes, where each box can hold any number of balls. Alice randomly chooses 3 balls and Bob randomly chooses 2 boxes. In how many ways can they make their choices such that the total number of colors of the chosen balls is equal to the total number of colors of the chosen boxes?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nTwo circles are tangent to each other. One circle has a radius of 4 and a center at the origin. The other circle has a radius of 6 and a center at the point (a, 0). Find a.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven a deck of cards numbered 1 through 20, players A and B take turns drawing cards until they have a total of 4 cards each. If player A's total score (sum of their card numbers) is greater than player B's score by a multiple of 5, then player A wins. Otherwise, player B wins. If the score difference is exactly 10, the game is a draw. Determine the initial card number such that, if player A draws it first, they can always win or draw, regardless of player B's strategy.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the range of values of $x$ for which the inequality $x^2 - 4x + 3 > 0$ holds true.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the volume of the set of points that are inside or within one unit of a right circular cone with a base radius of 2 units and a height of 3 units.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA concert hall has a capacity of 120 people, and ticket prices are $15.00 per person. On a Saturday evening, only 80 tickets were sold. By not selling out, how much revenue did the concert hall miss out on?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhat is the product of all values of $a$ such that the equation $x^2-ax+2a=0$ has a solution that is the reciprocal of an integer?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThere are 2017 unoccupied chairs in a row. Every minute, a person arrives and sits in one of them that is empty, and at the same instant, if it is occupied, a person in an adjacent chair stands up and leaves. What is the maximum number of people that can be sitting simultaneously in the row of chairs?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nTom has $m$ dollars in his piggy bank, where $m$ is a positive integer. If he spends $\\frac{1}{3}$ of his money, he will have a multiple of $7$. If he spends $\\frac{1}{7}$ of his money, he will have a multiple of $3$. What is the largest possible value of $m$ that satisfies these conditions?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n1. (8 points) Calculate: $2011-(9 \\times 11 \\times 11+9 \\times 9 \\times 11-9 \\times 11)=$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nHow many three-digit numbers can be expressed as the sum of three consecutive perfect cubes?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe set \\( \\{00, 01, \\cdots, 98, 99\\} \\) has a subset \\( X \\) that satisfies: in any infinite sequence of digits, there exist two adjacent digits that form an element of \\( X \\). What is the smallest number of elements that \\( X \\) must contain?\n(52nd Moscow Mathematical Olympiad problem)\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEmily plans to make a batch of cookies for her school bake sale. According to the recipe, she needs to purchase 3 cups of oatmeal, a cup of chocolate chips, a cup of nuts, and 3 eggs. The oatmeal costs $3, the chocolate chips cost $2, the nuts cost $4, and the eggs cost $1. After baking, she packs the cookies into 12 bags. She sells 4 bags at the bake sale, and when she returns home, she finds out that her little brother ate the remaining bags of cookies. How much did the amount her brother ate cost?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n15. Find all positive integers $n$, such that $n+36$ is a perfect square, and apart from 2 or 3, $n$ has no other prime factors.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhen the strawberries at Fruity Farm are ready for harvest, Miguel charges each interested picker $4 to access the strawberry fields. Once there, people pick as many strawberries as they wish, and then take them to Miguel for weighing and pricing. This year, the standard price of a pound of strawberries is $20. Miguel is a very generous man. He deducts the entrance charge from the cost of the harvest. Sally, Jenny and Moses have just finished their strawberry picking and paid $128 for their harvest. How many pounds of strawberries did they pick?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn a 50-question test with two marks for each question, Meghan learned that she scored 20 marks less than her friend Jose, who scored 40 more marks than their friend Alisson. The total score for the three in the test combined is 210. How many questions did Jose get wrong?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nMorgan rode her bike 5 blocks from her house to the park. She then walked 3 blocks to the store. Later, she came home the same way. How many blocks did Morgan travel in all?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nSimplify $49^{\\frac{1}{2}}-9^{\\frac{1}{2}}$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the number of positive integers $m \\le 2000$ such that $24m$ is a perfect cube.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nEmily is organizing a group trip to the beach for 10 friends. They booked a beach house for $4200 and plan to rent two surfboards for $300 each. If they decide to split the total cost evenly, how much will each person have to pay?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA round-robin tournament is being held with 5 teams. Each pair of teams plays each other once, and there are no ties. The probability of Team A beating Team B is 2/3, Team A beating Team C is 3/5, Team A beating Team D is 1/2, and Team A beating Team E is 4/7. If Team A wins all its games, what is the probability that it will win the tournament? Express your answer as a decimal rounded to the nearest hundredth.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nSimplify first, then evaluate: $\\left(x+3\\right)\\left(x-2\\right)+x\\left(4-x\\right)$, where $x=2$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA rectangular prism container with a rectangular base of 6 cm by 9 cm is designed to hold a specific amount of coffee. The container is to be made of a material that can only withstand a maximum height of 12 cm. What should be the dimensions of the container's rectangular base if the total volume of coffee it can hold needs to be 432 cubic cm? Express your answer to the nearest whole number.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the maximum value of $xy$ for positive integers $x$ and $y$ such that $x \\neq y$ and $2x + 3y = 120$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven a complex number $z$ satisfies $(1-i)z=2+2i$, where $i$ is the imaginary unit, find the value of $|z|$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nrobert ' s salary was decreased by 70 % and subsequently increased by 70 % . how much percentage does he lose ?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA store has three types of boxes: A, B, and C. Box A contains 12 large socks and 8 small socks, while boxes B and C each contain 8 large socks and 12 small socks. A customer randomly selects a box and then randomly selects a sock from that box. What is the probability that the customer selects two large socks in a row? Express your answer as a common fraction.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nJulia is a sales representative for a solar panel company, earning a commission of $50 for each panel set she sells. She is visiting a community with five streets, each with 10 houses. On the first street, she sold twice as many panel sets as on the fifth street. However, she made no sales on the second street, and the third street gave her only two sales. The fourth street provided her with the same number of sales as the first and fifth streets combined. If her total commission was $750, how many panel sets did she sell on the first street?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWilson's Cafe sold 8 more than three times the number of sandwiches that Thompson's Cafe sold. If Thompson's Cafe sold 20 sandwiches, how many sandwiches did Wilson's Cafe sell?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFind the positive integer m that makes the largest difference between the largest and smallest possible values of x in the equation:\n\n10x + 2m ≤ 35,\n\ngiven that x and m are both integers.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven that $\\tan α= \\sqrt {2}$, find $\\tan (α+ \\dfrac {π}{4})=$\\_\\_\\_\\_\\_\\_.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn the right circular cone $S-ABCD$, the base $ABCD$ is a rhombus with side length $4 \\sqrt {2}$, $\\angle BCD=60^{\\circ}$, $SC=2$, and $E$ is the midpoint of $BC$. If point $P$ moves on $SE$, find the minimum area of $\\triangle PCA$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven the operation defined as $a*b= \\begin{cases} a & (a\\leqslant b) \\\\ b & (a > b)\\end{cases}$, find the maximum value of the function $f(x)=1*2^{x}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA group of 8 friends, consisting of 4 couples, want to take a group photo. Each person must stand next to their partner, and the couples must alternate between standing on the left and right sides of the photo. How many different arrangements are possible if the photo is taken from the front, and reflections are considered the same arrangement?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nTask B-1.6. How many ordered pairs of integers $x, y, 0<x<y<10^{6}$ are there such that their arithmetic mean is exactly 8 greater than their geometric mean? (The geometric mean of numbers $a$ and $b$ is the number $\\sqrt{a \\cdot b}$.)\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet $a$ be a positive integer such that $3a \\equiv 1 \\pmod{101}$. Find the smallest possible value of $a+b$, where $b$ is a positive integer such that $ab \\equiv 1 \\pmod{100}$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn triangle ABC, the product of the sines of angles A and B is 1/3. What is the measure of angle C?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nGiven vectors $\\overrightarrow{OA}=(k,12,1)$, $\\overrightarrow{OB}=(4,5,1)$, $\\overrightarrow{OC}=(-k,10,1)$, and points $A$, $B$, $C$ are collinear, then $k=$ \\_\\_\\_\\_\\_\\_.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nThe height of a right triangle, dropped to its hypotenuse, divides the bisector of an acute angle in the ratio $4: 3$, counting from the vertex.\n\nFind the measure of this angle.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nA standard deck of 52 cards is randomly arranged. Determine the probability that the top three cards are all from different suits.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn triangle $ABC$, the sides opposite angles $A$, $B$, and $C$ are denoted by $a$, $b$, and $c$ respectively, and it is given that $\\cos A = \\frac{1}{4}$, and $b = 2c$. Find the value of $\\sin C$.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nFrom a set of 90 products numbered from 0, 1, 2, ..., 89, a systematic sampling method is used to draw a sample of size 9. If product number 36 is in the sample, then the largest number in the sample is ___.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIf the perimeter of the base of a right prism is $4$ and its height is $2$, then the surface area of the prism is ______.\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\n6. In rectangle $A B C D$, it is known that $A D=12, A B$ $=5, P$ is any point on side $A D$, $P E \\perp B D, P F$ $\\perp A C, E, F$ are the feet of the perpendiculars, respectively. Then, $P E+P F=$ $\\qquad$\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nWhat is the value of $a$ if $f(x) = 2x^2 + ax - 3$ and $f(f(1)) = 5$?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nIn a bookshelf, there are five books of different genres: romance, mystery, sci-fi, fantasy, and horror. The romance and mystery books are written by the same author, and the author insists that they be placed together. The sci-fi and fantasy books are part of a series and must be placed in a specific order (sci-fi first, then fantasy). The horror book can be placed anywhere, but it cannot be placed next to the romance book. In how many ways can the books be arranged on the shelf?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]

[ { "content": "You are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process is enclosed within <think> </think> tags, i.e. <think> reasoning process here </think>.\n\nLet $f(3x+2) = 5x - 3$. For what value of $x$ is $f(x) = 2x$?\n\nPlease reason step by step, and put your final answer within \\boxed{}", "role": "user" } ]