While reinforcement learning has unlocked unprecedented complex reasoning in large language models, it has also amplified their propensity for hallucination, creating a critical trade-off between capability and reliability. This work confronts this challenge by introducing a targeted RL framework designed to mitigate both intrinsic and extrinsic hallucinations across short and long-form question answering. We address extrinsic hallucinations (flawed internal knowledge) by creating a novel training set from open-ended conversions of TriviaQA. Concurrently, we tackle intrinsic hallucinations (unfaithfulness to context) by leveraging long-form texts from FineWeb in a fact-grounding reward scheme. To further bolster reliability, our framework explicitly rewards the model for refusing to answer unanswerable questions, thereby cultivating crucial cautiousness. Extensive experiments demonstrate that our methodology yields significant performance gains across a diverse suite of benchmarks, substantially reducing both hallucination types. Ultimately, this research contributes a practical framework for resolving the critical tension between advanced reasoning and factual trustworthiness, paving the way for more capable and reliable large language models.