While Large Language Models (LLMs) exhibit remarkable capabilities, they also introduce significant safety and privacy risks. Current mitigation strategies often fail to preserve contextual reasoning capabilities in risky scenarios. Instead, they rely heavily on sensitive pattern matching to protect LLMs, which limits the scope. Furthermore, they overlook established safety and privacy standards, leading to systemic risks for legal compliance. To address these gaps, we formulate safety and privacy issues into contextualized compliance problems following the Contextual Integrity (CI) theory. Under the CI framework, we align our model with three critical regulatory standards: GDPR, EU AI Act, and HIPAA. Specifically, we employ reinforcement learning (RL) with a rule-based reward to incentivize contextual reasoning capabilities while enhancing compliance with safety and privacy norms. Through extensive experiments, we demonstrate that our method not only significantly enhances legal compliance (achieving a +8.58% accuracy improvement in safety/privacy benchmarks) but also further improves general reasoning capability. For OpenThinker-7B, a strong reasoning model that significantly outperforms its base model Qwen2.5-7B-Instruct across diverse subjects, our method enhances its general reasoning capabilities, with +2.05% and +8.98% accuracy improvement on the MMLU and LegalBench benchmark, respectively.