{"taskset": {"n_runnable": 0, "name": null, "url_data": null, "catalog_id": null, "owner_type": null, "cited_by": null, "taskset": "ineqmath", "domain": "science-math", "task_kind": null, "environment": null, "grading": null, "path": "datasets/ineqmath", "n_single_container": 100, "n_tasks": 100, "domain_raw": null, "sample_instruction": "Solve the following problem. Reason step by step, create the file /app/answer.txt, and put your final answer there. \n\nTask description: Please solve the problem with clear, rigorous, and logically sound steps. At the end of your response, state your answer in exactly this format: 'The answer is $C=X$', where X is your calculated numerical bound value. Example: 'The answer is $C=1$'.\n\nProblem: Let $a, b, c > 0$. Determine the largest constant $C$ such that the following inequality holds for all $a, b, c$:\n\n$$\n\\frac{a+b+c}{\\sqrt[3]{a b c}}+\\frac{8 a b c}{(a+b)(b+c)(c+a)} \\geq C.\n$$\n\nSolution:", "owner_org": null, "url_repo": null, "url_paper": null, "license": null, "languages": [], "difficulties": {"difficult": 100}, "categories": ["math reasoning"]}, "tasks": [{"agent_timeout": 3600, "category": "math reasoning", "compose": false, "difficulty": "difficult", "language": "", "oracle": null, "runnable": false, "tags": ["IneqMath", "multiple-choice", "bound"], "task": "0", "taskset": "ineqmath"}, {"agent_timeout": 3600, "category": "math reasoning", "compose": false, "difficulty": "difficult", "language": "", "oracle": null, "runnable": false, "tags": ["IneqMath", "multiple-choice", "bound"], "task": "1", "taskset": "ineqmath"}, {"agent_timeout": 3600, "category": "math reasoning", "compose": false, "difficulty": "difficult", "language": "", "oracle": null, "runnable": false, "tags": 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