Recall that a problem is NP-complete if it is both in NP and NP-hard. Start by verifying if the problem you're analyzing belongs to NP.

To prove NP-hardness, consider reducing a known NP-complete problem (like SAT or 3-SAT) to your problem in polynomial time. Construct a polynomial-time reduction that transforms instances of the known NP-complete problem into instances of your problem while preserving the answer.

If direct reduction seems complex, try leveraging the Cook-Levin theorem, which states that SAT is NP-complete. Reduce SAT to your problem by constructing a polynomial-time algorithm that converts any boolean formula into an instance of your problem such that the formula is satisfiable if and only if the constructed instance has a solution.