Yes, there are various approaches like tree-of-thought. They don't fundamentally solve the problem because there are just too many paths to explore and inference is just too slow and too expensive to explore 10,000 or 100,000 paths just for basic problems that no one wanted to solve anyway.
The problem with solving such problems with LLMs is that if the solution to the problem is unlike problems seen in training, the LLM will almost every time take the wrong path and very likely won't even think of the right path at all.
The AI really does need to understand why the paths it tried failed in order to get insight into what might work. That's how humans work (well, one of many techniques we use). And despite what people think, LLMs really don't understand what they are doing. That's relatively easy to demonstrate if you get an LLM off distribution. They will double down on obviously erroneous illogic, rather than learn from the entirely new situation.
The problem with solving such problems with LLMs is that if the solution to the problem is unlike problems seen in training, the LLM will almost every time take the wrong path and very likely won't even think of the right path at all.
The AI really does need to understand why the paths it tried failed in order to get insight into what might work. That's how humans work (well, one of many techniques we use). And despite what people think, LLMs really don't understand what they are doing. That's relatively easy to demonstrate if you get an LLM off distribution. They will double down on obviously erroneous illogic, rather than learn from the entirely new situation.