Abstract: Deploying Large Language Models (LLMs) in healthcare requires robust performance across two complementary dimensions - diagnostic reasoning: the convergent, evidence-driven task of inferring a patient's condition from clinical data to produce a diagnosis, and clinical healthcare reasoning: the broader, navigational judgment required to communicate, plan, and adapt across multi-turn clinical interactions where a single correct answer may not exist. Recent benchmarks such as HealthBench and MedXpertQA reveal persistent weaknesses in both areas, exposing failures in complex diagnostic scenarios and limitations in contextual, patient-centered dialogue. We introduce a sequential training framework that targets these facets using synthetic data and rubric-based reinforcement learning. First, we improve diagnostic reasoning using MedBullets-derived questions with rule- and rubric-guided Reinforcement Learning (RL). We then shift to clinical reasoning by generating 5.3k synthetic multi-turn scenarios, each paired with multi-dimensional rubrics to comprehensively assess the response. This approach yields over 10% improvement on MedXpertQA, and our 30B model achieves 50.1% accuracy on HealthBench-Hard, surpassing proprietary baselines including GPT-5 (thinking). Our results show that targeted synthetic datasets and rubric-based training can systematically improve both diagnostic and interactive clinical reasoning in medical LLMs.