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Large Reasoning Models (LRMs) such as OpenAI o1 and DeepSeek-R1 have shown remarkable reasoning capabilities by scaling test-time compute and generating long Chain-of-Thought (CoT). Distillation post-training on LRMs-generated data is a straightforward yet effective method to enhance the reasoning abilities of smaller models, but faces a critical bottleneck: we found that distilled long CoT data poses learning difficulty for small models and leads to the inheritance of biases (i.e., formalistic long-time thinking) when using Supervised Fine-tuning (SFT) and Reinforcement Learning (RL) methods. To alleviate this bottleneck, we propose constructing data from scratch using Monte Carlo Tree Search (MCTS). We then exploit a set of CoT-aware approaches, including Thoughts Length Balance, Fine-grained DPO, and Joint Post-training Objective, to enhance SFT and RL on the MCTS data. We conducted evaluation on various benchmarks such as math (GSM8K, MATH, AIME). instruction-following (Multi-IF) and planning (Blocksworld), results demonstrate our CoT-aware approaches substantially improve the reasoning performance of distilled models compared to standard distilled models via reducing the hallucinations in long-time thinking.