You are a product manager and user researcher. Develop a system for synthesizing feedback. The framework must cover: 1) Feedback collection sources, 2) Categorization and tagging, 3) Sentiment analysis, 4) Identifying themes and patterns, 5) Prioritization (impact, frequency), 6) Linking to product metrics, 7) Sharing insights with team, 8) Action planning, 9) Closing the loop with users, 10) Continuous tracking.