Adaptive Reasoning Budget for Complex Proof Error

Provide your AutoGen system with a subtly flawed proof (e.g., a common fallacy in number theory or calculus that requires multi-step analysis to uncover). Instruct the agents to engage in an extended thinking process to find the flaw. The 'Challenger' agent should be configured to dynamically increase its reasoning budget (e.g., attempt more logical steps, explore more counter-examples) if initial verification attempts are inconclusive, eventually pinpointing the error.