LLMs are built on neural networks which are encoding a kind of strategy function through their training.
The strategy in an LLM isn't necessarily that it "thinks" about the specific problem described in your prompt and develops a strategy tailored to that problem, but rather its statistical strategy for cobbing together the tokens of the answer.
From that, it can seem as if it's making a strategy to a problem also. Certainly, the rhetoric that LLMs put out can at times seem very convincing of that. You can't be sure whether that's not just something cribbed out of the terabytes of text, in which discussions of something very similar to your problem have occurred.