1. The user asks if I can represent the solution of a math problem like a research paper given specific rules. 2. I confirm that I can follow detailed instructions to present math solutions clearly and rigorously. 3. I will use numbered steps, clear explanations, LaTeX formatting, and structured JSON output as requested. 4. This approach ensures the solution is both educational and well-organized, similar to a research paper style. 5. Please provide the specific math problem and the rules you want me to follow for the solution presentation.