As large language models empower healthcare, intelligent clinical decision support has developed rapidly. Longitudinal electronic health records (EHR) provide essential temporal evidence for accurate clinical diagnosis and analysis. However, current large language models have critical flaws in longitudinal EHR reasoning. First, lacking fine-grained statistical reasoning, they often hallucinate clinical trends and metrics when quantitative evidence is textually implied, biasing diagnostic inference. Second, non-uniform time series and scarce labels in longitudinal EHR hinder models from capturing long-range temporal dependencies, limiting reliable clinical reasoning. To address the above limitations, this work presents the Probabilistic Chain-of-Thought Completion Agent (COTCAgent), a hierarchical reasoning framework for longitudinal electronic health records. It consists of three core modules. The Temporal-Statistics Adapter (TSA) converts analytical plans into executable code for standardized trend output. The Chain-of-Thought Completion (COTC) layer leverages a symptom-trend-disease knowledge base with weighted scoring to evaluate disease risk, while the bounded completion module acquires structured evidence through standardized inquiries and iterative scoring constraints to ensure rigorous reasoning. By decoupling statistical computation, feature matching, and language generation, the framework eliminates reliance on complex multi-modal inputs and enables efficient longitudinal record analysis with lower computational overhead. Experimental results show that COTCAgent powered by Baichuan-M2 achieves 90.47% Top-1 accuracy on the self-built dataset and 70.41% on HealthBench, outperforming existing medical agents and mainstream large language models. The code is available at https://github.com/FrankDengAI/COTCAgent/.