The problem I want to solve is: [FILL IN YOUR PROBLEM].
Please use first principles to break it down to the most fundamental level, distinguishing: 1. Established, unavoidable basic facts; 2. Habitually accepted but unverified assumptions; 3. The goal you truly want to achieve; 4. Real-world resources and constraints.
Temporarily set aside industry conventions and existing solutions, and re-derive feasible paths only from basic facts, goals, and constraints.
Finally, please output: 1. The parts of the original solution that only patch the surface; 2. A new path re-derived from basic facts; 3. The preconditions for this path to hold; 4. The first step to verify it.
