Despite strong performance in medical question answering, large language models remain limited in clinical cold-start settings, where little patient information is initially available and key evidence must be acquired through dialogue. This requires models to decide what to ask under a limited turn budget, balancing broad history taking with targeted clarification of high-risk cues. To address the aforementioned challenges, we propose **MedCIA**, a two-stage framework for improving clinical information acquisition. First, it reconstructs patient records into structured inquiry trajectories, enabling supervised learning of expert-guided information-seeking intents and the breadth-depth trade-off in clinical questioning. Second, it refines the policy with Adaptive Tree Policy Optimization (ATPO), an uncertainty-aware reinforcement learning procedure that allocates rollout computation to ambiguous dialogue states in a profile-anchored patient simulator. Furthermore, we curate a multi-turn dataset (MedIntake) for active clinical intake with progressive patient information disclosure and diverse inquiry strategies. Experiments on an EHR-derived benchmark show that **MedCIA** improves importance-weighted coverage, early acquisition, and cost control under controlled simulation.