Large language models are increasingly becoming part of software engineering education, including activities involving empirical software engineering and evidence synthesis. This paper reports an educational experience involving the integration of reflective LLM use into an empirical methods assignment in a third-year software architecture course. Students were asked to develop a short research paper using either a rapid review or a gray literature review methodology and to disclose how LLMs were used throughout the assignment. We analyzed 146 student disclosure statements using a cross-analysis process combining LLM-assisted categorization with manual verification and refinement by the researchers. The reflections describe how students incorporated LLMs during activities such as brainstorming, methodological clarification, organization of findings, and writing refinement, while also reporting concerns regarding inaccuracies and verification of generated content. This experience report discusses lessons learned and educational implications for integrating AI-assisted technologies into empirical software engineering education.