You have to DO what no one has THOUGHT of yet.
...you just have to do what no one has thought of yet. You'll notice I have two different words there: You have to DO what know one has THOUGHT of yet. Sometimes they HAVE thought of it--but they've dismissed it. "That probably won't help enough to justify the hours," "That's probably unrelated", etc, but no one has actually DONE it.
In Korea, I found myself learning Korean. Just a few phrases--but it dramatically unbent the customer. I found myself making 20 phone calls to track down the ONE PERSON in a dusty little office on the Duwamish, the ONE person who had ownership of the flight instruction manuals, and tell me how many pages those manuals had, because we got credit for $100/page of documentation. In my career, I've lost count of the times that people have said, "No one has ever asked me that before."
Good problem solving takes detective work, forensics, and data analysis, and a quiver of wide-ranging skills doesn't hurt, either. I know a little about databases, a little about coding, a little bit about materials testing, a little bit about regulatory compliance. I speak a smattering of languages, from foreign ones to government jargon.