We present a novel framework addressing a critical vulnerability in Large Language Models (LLMs): the prevalence of factual inaccuracies within intermediate reasoning steps despite correct final answers. This phenomenon poses substantial risks in high-stakes domains including healthcare, legal analysis, and scientific research, where erroneous yet confidently presented reasoning can mislead users into dangerous decisions. Our framework integrates three core components: (1) a specialized fact-checking classifier trained on counterfactually augmented data to detect subtle factual inconsistencies within reasoning chains; (2) an enhanced Group Relative Policy Optimization (GRPO) reinforcement learning approach that balances factuality, coherence, and structural correctness through multi-dimensional rewards; and (3) a mechanistic interpretability method examining how factuality improvements manifest in model activations during reasoning processes. Extensive evaluation across multi state-of-the-art models reveals concerning patterns: even leading models like Claude-3.7 and GPT-o1 demonstrate reasoning factual accuracy of only 81.93% and 82.57% respectively. Our approach significantly enhances factual robustness (up to 49.90% improvement) while maintaining or improving performance on challenging benchmarks including Math-500, AIME-2024, and GPQA. Furthermore, our neural activation-level analysis provides actionable insights into how factual enhancements reshape reasoning trajectories within model architectures, establishing foundations for future training methodologies that explicitly target factual robustness through activation-guided optimization.