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Column name 'Points $A$ and $B$ are selected on the graph of $y = -\frac{1}{2}x^2$ so that triangle $ABO$ is equilateral. Find the length of one side of triangle $ABO$. [asy]
size(150);
draw( (-4, -8) -- (-3.4641, -6)-- (-3, -9/2)-- (-5/2, -25/8)-- (-2,-2)-- (-3/2, -9/8) -- (-1, -1/2) -- (-3/4, -9/32) -- (-1/2, -1/8) -- (-1/4, -1/32) -- (0,0) -- (1/4, -1/32) -- (1/2, -1/8) -- (3/4, -9/32) -- (1, -1/2) -- (3/2, -9/8)-- (2,-2)-- (5/2, -25/8)--(3, -9/2)-- (3.4641, -6) -- (4, -8) , Arrows);
draw( (-3.4641, -6...' is too long. It should be less than 500 characters.
Error code: TooLongColumnNameError
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Citation
@article{zhang2024llama,
title={LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning},
author={Zhang, Di and Wu, Jianbo and Lei, Jingdi and Che, Tong and Li, Jiatong and Xie, Tong and Huang, Xiaoshui and Zhang, Shufei and Pavone, Marco and Li, Yuqiang and others},
journal={arXiv preprint arXiv:2410.02884},
year={2024}
}
@article{zhang2024accessing,
title={Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B},
author={Zhang, Di and Li, Jiatong and Huang, Xiaoshui and Zhou, Dongzhan and Li, Yuqiang and Ouyang, Wanli},
journal={arXiv preprint arXiv:2406.07394},
year={2024}
}
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