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olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "32", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "10:00", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "f(x)=x^{2}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "1", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "(C)", "style": "rule" }
{ "index": -1, "split": "default" }
amc_aime
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "21", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "10", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "B", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\sqrt{13}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "4641", "style": "rule" }
{ "index": -1, "split": "default" }
amc_aime
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "47", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "29970", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "50", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "2", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "-1.5", "style": "rule" }
{ "index": -1, "split": "default" }
aops_forum
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": " k = 2 ", "style": "rule" }
{ "index": -1, "split": "default" }
aops_forum
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "3, 7", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\Gamma", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "10", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "D", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "142857", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "3n", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "8", "style": "rule" }
{ "index": -1, "split": "default" }
amc_aime
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "490", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\sqrt{13}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{77}{135}", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "f(x)=0", "style": "rule" }
{ "index": -1, "split": "default" }
amc_aime
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "131", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{2\\sqrt{3}}{3}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{224}{15}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "30", "style": "rule" }
{ "index": -1, "split": "default" }
number_theory
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "126", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "A", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "10", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "5", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "a_{n}=\\frac{2^{2n-1}+3\\cdot2^{n-1}+1}{3\\cdot2^{2n-1}}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "2", "style": "rule" }
{ "index": -1, "split": "default" }
aops_forum
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "37^2", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{32}{75}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "Thursday", "style": "rule" }
{ "index": -1, "split": "default" }
aops_forum
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "1018081", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "B", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "2^{n}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "1", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "12", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{Ak}{3(1+\\sqrt{1+k^{2}})}\\sqrt{\\frac{A}{\\pi(1+\\sqrt{1+k^{2}})}}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "602", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{1}{2}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "16798320", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "320", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "12\\pi", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{2015}{2013}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "27", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "15-\\sqrt{125},\\quad\\sqrt{125}-5", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "B", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "D", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "B", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "2.4", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "D", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "C", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "6", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "200", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "14", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "C", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "3\\sqrt{3}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads_ref
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "a=b=c=d=5", "style": "rule" }
{ "index": -1, "split": "default" }
amc_aime
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "252", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\sqrt{\\frac{12}{n(n^{2}-1)}}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "105263157894736842", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "0", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "13205", "style": "rule" }
{ "index": -1, "split": "default" }
amc_aime
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "943", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "m^2 + m", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "60", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "D", "style": "rule" }
{ "index": -1, "split": "default" }
aops_forum
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\text{Alice}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{\\sqrt{15}}{2}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{1}{2}", "style": "rule" }
{ "index": -1, "split": "default" }
aops_forum
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{22}{703}", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "B", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "13", "style": "rule" }
{ "index": -1, "split": "default" }
inequalities
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "13 x^{3} + 5 x^{2} + 12 x + 3", "style": "rule" }
{ "index": -1, "split": "default" }
aops_forum
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "9", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "144\\mathrm{~}^{3}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "(\\sqrt{P_{1}}+\\sqrt{P_{2}})^{2}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\frac{e^{x}\\sqrt{e^{2x}-1}-\\sqrt{e^{-2x}-1}}{\\sqrt{1-e^{-2x}}\\cdot\\sqrt{1-e^{2x}}}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "20", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\left[1-\\frac{\\sqrt{2}}{2}, 1\\right]", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "[3, \\sqrt[3]{36}]", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "10", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "108", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "0", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "C", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "2036", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "E", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "1972", "style": "rule" }
{ "index": -1, "split": "default" }
amc_aime
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "\\textbf{(A)}", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "198", "style": "rule" }
{ "index": -1, "split": "default" }
cn_contest
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "50^{\\circ}", "style": "rule" }
{ "index": -1, "split": "default" }
olympiads
[ { "content": "Your task is to follow a systematic, thorough reasoning process before providing the final solution. This involves analyzing, summarizing, exploring, reassessing, and refining your thought process through multiple iterations. Structure your response into two sections: Thought and Solution. In the ...
{ "ground_truth": "200", "style": "rule" }
{ "index": -1, "split": "default" }
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