{"task": {"agent_timeout": 600, "task": "omnimath_563", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet $\\triangle A B C$ be a triangle inscribed in a unit circle with center $O$. Let $I$ be the incenter of $\\triangle A B C$, and let $D$ be the intersection of $B C$ and the angle bisector of $\\angle B A C$. Suppose that the circumcircle of $\\triangle A D O$ intersects $B C$ again at a point $E$ such that $E$ lies on $I O$. If $\\cos A=\\frac{12}{13}$, find the area of $\\triangle A B C$.\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": []}