Integrating Large Language Models (LLMs) into complex software systems enables the generation of human-understandable explanations of opaque AI processes, such as automated task planning. However, the quality and reliability of these explanations heavily depend on effective prompt engineering. The lack of a systematic understanding of how diverse stakeholder groups formulate and refine prompts hinders the development of tools that can automate this process. We introduce COMPASS (COgnitive Modelling for Prompt Automated SynthesiS), a proof-of-concept self-adaptive approach that formalises prompt engineering as a cognitive and probabilistic decision-making process. COMPASS models unobservable users' latent cognitive states, such as attention and comprehension, uncertainty, and observable interaction cues as a POMDP, whose synthesised policy enables adaptive generation of explanations and prompt refinements. We evaluate COMPASS using two diverse cyber-physical system case studies to assess the adaptive explanation generation and their qualities, both quantitatively and qualitatively. Our results demonstrate the feasibility of COMPASS integrating human cognition and user profile's feedback into automated prompt synthesis in complex task planning systems.