One step might be to try and understand the basic principles behind what makes a LLM function. The Youtube channel 3blue1brown has at least one good video on transformers and how they work, and perhaps that will help you understand that "reasoning" is a very broad term that doesn't necessarily mean thinking. What is going on inside a LLM is fascinating and amazing in what does manage to come out that's useful, but like any tool it can't be used for everything well, if at all.