Large Reasoning Models (LRMs) often exhibit an efficiency-accuracy trade-off, leading to errors from insufficient self-diagnosis and correction during inference. Existing reasoning methods frequently lack internal feedback for refining generated steps. To address this, we propose the Reflective Reasoning System (RRS), an inference-time framework integrating explicit self-diagnosis and self-correction loops into LRM reasoning. RRS strategically employs meta-cognitive tokens to guide the model through initial reasoning, critical self-assessment of potential flaws, and subsequent revision, all without requiring additional training or fine-tuning. Our extensive experiments across diverse open-source models and challenging benchmarks spanning mathematics, code generation, and scientific reasoning demonstrate that RRS consistently achieves significant accuracy improvements compared to baseline models and competitive inference-time enhancement methods. Human evaluations and ablation studies further confirm the efficacy of these distinct self-diagnosis and self-correction phases, highlighting RRS's ability to unlock LRMs' latent reflective capabilities for more robust and accurate solutions.