Recent reasoning-centric Large Language Models (LLMs) have made significant strides, yet they predominantly operate on a passive-inference pattern that assumes complete information. In contrast, real-world clinical intelligence is inherently an iterative investigative process requiring strategic evidence acquisition. To bridge this gap, we formalize medical diagnosis as an Iterative Evidence-Seeking Task. We leverage Reinforcement Learning with Verifiable Rewards (RLVR) to elicit intrinsic reasoning within a closed-loop environment, guided by a novel suite of rewards that enforce diagnostic precision and examination consistency. To facilitate this, we introduce the Retrieval-Augmented Generation-based Examination Simulator (RAGES), a high-fidelity clinical oracle that provides realistic, knowledge-grounded follow-up evidence. Empirical results across diverse datasets demonstrate that our framework enables LLMs to transition from passive responders to autonomous assistants. Notably, our model demonstrates comparable performance to larger and reasoning-enhanced baselines, while RAGES proves superior to vanilla LLMs in generating biologically plausible clinical feedback.

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