Emotion cause analysis is a critical topic in natural language processing. Key tasks include emotion cause extraction (ECE), emotion-cause pair extraction (ECPE), social emotion cause identification (SECI) as well as social emotion mining and its cause identification (SEMCI). While current emotion cause analysis methods often focus on task-specific model design, they tend to overlook the underlying common ground across these tasks rooted in cognitive emotion theories, in particular, the cognitive structure of emotions. Drawing inspiration from this theory, in this paper, we propose a unified model capable of tackling diverse emotion cause analysis tasks, which constructs the emotion cognitive structure through LLM-based in-context learning. To mitigate the hallucination inherent in LLMs, we introduce a self-promote mechanism built on iterative refinement. It dynamically assesses the reliability of substructures based on their cognitive consistency and leverages the more reliable substructures to promote the inconsistent ones. Experimental results on multiple emotion cause analysis tasks ECE, ECPE, SECI and SEMCI demonstrate the superiority of our unified model over existing SOTA methods and LLM-based baselines.