As generative artificial intelligence becomes increasingly integrated into educational, professional, and creative domains, there is a growing need to move beyond systems that merely provide answers toward those that actively support deeper reasoning and innovation. This paper proposes a theoretical framework that combines the principles of TRIZ, a systematic methodology for inventive problem solving, with the Socratic method, a dialogic approach rooted in guided inquiry and critical reflection. The resulting hybrid model aims to transform AI from a knowledge-delivery system into a facilitator of structured and reflective problem-solving. The framework consists of five interdependent modules: input interpretation, large language model processing, Socratic dialogue generation, TRIZ-based reasoning, and adaptive feedback management. These components work collaboratively to guide users through stages of problem reframing, contradiction identification, ideality orientation, and solution exploration. The system can be implemented using either as an integrated or modular architecture, with opportunities for fine-tuning language models to support question-driven reasoning and embedding domain-specific knowledge through structured representations such as TRIZ contradiction matrices. Evaluation strategies emphasize a combination of quantitative metrics, qualitative analysis, and controlled experimentation to assess the framework’s impact on cognitive engagement and inventive thinking. Potential applications are explored in both educational and professional contexts, with attention to integration with explainable AI and multimodal interfaces. Ethical considerations regarding neutrality, transparency, and user agency are also addressed. By synthesizing structured innovation theory with pedagogically grounded dialogue techniques, this framework contributes to the development of AI systems that not only respond to queries but also enhance human reasoning and creativity.