While Chain-of-Thought (CoT) prompting empowers Large Language Models (LLMs), ensuring reasoning reliability remains an open challenge. Contrary to the prevailing cascading failure hypothesis which posits that early errors are most detrimental, we identify a counter-intuitive phenomenon termed \textbf{Late-Stage Fragility}: errors introduced in later reasoning stages are significantly more prone to corrupting final answers. To address this, we introduce ASCoT (Adaptive Self-Correction Chain-of-Thought), a method harmonizing efficiency with robust verification. ASCoT first employs semantic pruning to compress redundant steps, then utilizes an Adaptive Verification Manager (AVM) to prioritize high risk, late-stage steps via a positional impact score, triggering a Multi-Perspective Self-Correction Engine (MSCE) only when necessary. Experiments on GSM8K and MATH-500 demonstrate that ASCoT effectively reallocates computational resources: it reduces token usage by 21\%--30\% for LLaMA-3.1-8B with negligible accuracy drops ($<1.8\%$), achieving a superior trade-off between inference efficiency and reasoning fidelity.