Testing LLM reasoning abilities with SAT is not an original idea; there is a recent research that did a thorough testing with models such as GPT-4o and found that for hard enough problems, every model degrades to random guessing. But I couldn't find any research that used newer models like I used. It would be nice to see a more thorough testing done again with newer models.
It then uses the standard Dijkstra algorithm on the detailed local map within your start cluster to find the best paths from your actual start location to all border points of that starting cluster.
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