Problem-solving in design is less about the screens, and more about the relationship of the person using your solution to what they consider a successful outcome.
Early in my career, I designed screens by leveraging my background in debate. I would take a series of observations, outline a plan and then describe projected benefits. It was very efficient and structured, and had it's justifications built in. The problem was, as in a debate, there are always two sides, and having the design advocate for one solution based on cherry-picked observations is missing the point. We are not our users, and need to fall in love with the problem, not the solution.
More recently, my problem solving has more to do with storytelling. I need to understand the characters, their background, their motivations, what is holding them back and what they dream of. Not every character is the same, but every character is the hero of their own journey, and our role as designers is that of the mentor, guiding them through their experience to achieve their goals.
Finding that journey, and understanding I am not at the center of that journey, is critical. Once you really understand the journey, laying out screens to support it is nearly secondary.
