{"task": {"agent_timeout": 600, "task": "omnimath_435", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nJeffrey writes the numbers 1 and $100000000=10^{8}$ on the blackboard. Every minute, if $x, y$ are on the board, Jeffrey replaces them with $\\frac{x+y}{2} \\text{ and } 2\\left(\\frac{1}{x}+\\frac{1}{y}\\right)^{-1}$. After 2017 minutes the two numbers are $a$ and $b$. Find $\\min (a, b)$ to the nearest integer.\n\n## Instructions\n\nSolve the mathematical problem above and write your final answer to `/workspace/answer.txt`.\n\n**Important**: Write only your final answer to the file, not the full solution process.\n\n### Guidelines\n\n- Provide your final numerical answer or mathematical expression\n- Write the answer as plain text (no special formatting needed)\n- Be precise and clear in your answer\n- The answer should directly respond to what the problem asks for\n\n### Example\n\nIf the problem asks \"What is 2 + 2?\", your answer file should contain:\n\n```\n4\n```\n\nYour answer will be evaluated against the correct solution using an automated grading system.\n", "memory": "", "runnable": false, "difficulty": "hard", "language": "", "cpus": "", "instruction_truncated": false, "category": "math", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "omnimath", "tags": ["omni-math"]}, "runs": []}