While Audio Language Models (ALMs) demonstrate strong semantic understanding, they struggle with complex affective interactions. Specifically, textual semantic dominance often overshadows acoustic nuances, and a lack of cognitive depth leads to generic, emotion-agnostic responses. We propose CogAudio-LLM\footnote{ \urlstyle{same} https://github.com/zxzhao0/CogAudio-LLM, a novel cognitive affective reasoning framework. To mitigate semantic dominance, we build LIME-440K, a ``lexically-identical, multi-emotion'' dataset designed to facilitate acoustic-semantic decoupling. We introduce EIPS, a 4-step Chain-of-Thought (CoT) mechanism incorporating psychological reasoning. For inference efficiency, multi-stage training explicitly establishes EIPS via supervised fine-tuning, then distills this logic into an implicit generation process. Finally, we design DR-SAPO (Dual-Route Soft Adaptive Policy Optimization) to dynamically balance the logical rigor of the CoT with the empathetic quality of the direct response.