The headline question here alone gets at what is the biggest widespread misunderstanding of LLMs, which causes people to systematically doubt and underestimate their ability to exhibit real creativity and understanding based problem solving. At it's core an LLM is a sort of "situation specific simulation engine." You setup a scenario, and it then plays it out with it's own internal model of the situation, trained on…
"Sort of" is doing Sisisyphian levels of heavy lifting here. LLMs are statistical models trained on vast amounts of symbols to predict the most likely next symbol, given a sequence of previous symbols. LLMs may appear to exhibit "real creativity", "understand" problem solving (or anything else), or serve as "simulation engines", but it's important to understand that they don't currently do any of those things.