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Cognitive impairment is becoming a major public health challenge. Cognitive Stimulation Therapy (CST) is an effective intervention for cognitive impairment, but traditional methods are difficult to scale, and existing digital systems struggle with group dialogues and cognitive stimulation principles. While Large Language Models (LLMs) are powerful, their application in this context faces key challenges: cognitive stimulation dialogue paradigms, a lack of therapeutic reasoning, and static-only user modeling. To address these issues, we propose a principle-driven adaptive policy actualized through a Group Cognitive Stimulation Dialogue (GCSD) system. We first construct a dataset with over 500 hours of real-world CST conversations and 10,000+ simulated dialogues generated via our Principle-Guided Scenario Simulation strategy. Our GCSD system then integrates four core modules to overcome LLM limitations: (i) a multi-speaker context controller to resolve role confusion; (ii) dynamic participant cognitive state modeling for personalized interaction; (iii) a cognitive stimulation-focused attention loss to instill cognitive stimulation reasoning; and (iv) a multi-dimensional reward strategy to enhance response value. Experimental results demonstrate that GCSD significantly outperforms baseline models across various evaluation metrics. Future work will focus on long-term clinical validation to bridge the gap between computational performance and clinical efficacy.