Large language models (LLMs) are getting smarter, but their size is a problem. Distilling their knowledge into smaller models is crucial for wider access, but current methods struggle. They often focus on mimicking answers rather than truly understanding the reasoning process, especially when faced with unfamiliar tasks. Think of it like a student memorizing answers for a test instead of grasping the underlying concepts. They might do well on that specific test, but struggle when the questions change. This research introduces a clever new technique called Cascading Decomposed CoTs Distillation (CasCoD). It breaks down the learning process into two stages. First, the smaller model learns the "chain of thought" (CoT), the step-by-step reasoning, without seeing the final answer. This prevents it from taking shortcuts based on superficial patterns. Then, armed with this reasoning skill, it learns to connect the rationale to the correct answer. This two-step approach forces the model to focus on the "why" behind the answer, not just the "what." The results are impressive. CasCoD significantly outperforms existing methods, showing a remarkable ability to generalize its reasoning to new, unseen problems. This breakthrough has big implications for the future of AI. Smaller, more efficient models with powerful reasoning capabilities could revolutionize everything from chatbots to scientific discovery. While challenges remain, like the potential for inheriting biases from the larger models, this research opens exciting new avenues for making AI more accessible and effective.