用分阶段稀疏路由机制，让大模型高效协同专家诊断。

Complex clinical reasoning requires models to update diagnostic hypotheses as new evidence emerges and to coordinate different medical specialities under limited consultation resources. Existing LLM-based clinical reasoning systems typically perform single-pass prediction or rely on fixed multi-agent workflows, making expert participation either static or unnecessarily exhaustive. We propose Sparse Multi-Stage Expert-Agent Routing, a language-based clinical reasoning framework that models diagnosis as a stage-wise routing process. Given progressively available clinical evidence derived from multiple modalities, the framework maintains an evolving case state and adaptively activates a sparse set of medical expert agents, supported by expert-specific memory across stages. To evaluate free-text diagnostic conclusions beyond surface similarity, we further introduce ClinFEScore, a fact-aware semantic evaluation protocol for clinical reasoning outputs. On reconstructed multi-stage cases from MAC and AgentClinic-NEJM, our framework reduces the average number of activated experts from 17.0 to 3.0 whilst maintaining strong fact-level diagnostic quality. On 200 real-world hospital MDT cases, ClinFEScore correlates strongly with clinician judgements (Spearman's $ρ=0.81$; Pearson's $r=0.87$), whilst our method achieves 91.5\% clinician-verified diagnostic accuracy with approximately five expert-agent/LLM calls per case. These results support sparse stage-wise coordination as an efficient and clinically relevant approach to LLM-based clinical reasoning.