With the rapid advancement of artificial intelligence (AI) systems and large language models (LLMs), these technologies are increasingly used to generate content, provide answers, and engage in meaningful conversations. However, a significant gap remains: AI systems often lack the ability to reflect on their own behavior or reason critically about their responses. This paper introduces and explores the concept of reflective governance in LLM-based systems, presenting an architecture designed to enable these models to evaluate and refine their outputs, promoting more thoughtful and trustworthy interaction.