There’s no right or wrong answer here; not all UX designers have the same methods and strategies, and that’s absolutely fine. The interviewer just wants to see that you have a well thought-out approach to your work.
I think the whole point of user experience is that one focuses on the user first. Of course, one can’t lose sight of the business parameters. I imagine it’s a tricky path sometimes.
In my experience UX is a balancing act between evidence-based user needs and business needs, which are sometimes based on evidence and sometimes based on organizational politics.
What you’re always searching for is that sweet spot between what users want to accomplish and what the business wants to guide them toward.
So solving problems is first figuring out what problem we’re trying to solve, then figuring out if that is actually the problem we’re trying to solve (e.g. the business cares and users don’t), and then figuring out how big a problem it is.