Design and apply a comprehensive knowledge synthesis methodology to a complex domain with conflicting information (such as nutrition science debates, economic policy approaches, or climate change mitigation strategies). Your response must include: 1) Methodology description with theoretical foundation, 2) Systematic approach to source identification and quality assessment, 3) Framework for reconciling conflicting information and identifying nuance, 4) Method for identifying knowledge gaps and research needs, 5) Application of your methodology to a specific complex question, 6) Synthesized findings with confidence levels, and 7) Limitations of your methodology and potential refinements.