{"task": {"agent_timeout": 3600, "task": "66", "verifier_timeout": 3600, "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 (Letter) Symbol', where Letter is one of the given options. Example: 'The answer is (A) $\\leq$'.\n\nProblem: Let $a, b, c > 0$ be positive real numbers such that\n$$\n\\frac{1}{1+a} + \\frac{1}{1+b} + \\frac{1}{1+c} = 2.\n$$\n\nConsider the following inequality:\n$$\n2(2ab + 3bc + ca) \\quad () \\quad \\sqrt{ab} + \\sqrt{bc} + \\sqrt{ca}.\n$$\n\nDetermine the correct inequality relation to fill in the blank.\n\nOptions:\n\n(A) $\\leq$ \n\n(B) $\\geq$\n\n(C) $=$ \n\n(D) $<$\n\n(E) $>$\n\n(F) None of the above\n\nSolution:", "memory": "", "runnable": false, "difficulty": "difficult", "language": "", "cpus": "", "instruction_truncated": false, "category": "math reasoning", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "ineqmath", "tags": ["IneqMath", "multiple-choice", "relation"]}, "runs": []}