An LLM base model isn't trained for abstract thinking, but it still ends up developing abstract thinking internally - because that's the easiest way for it to mimic the breadth and depth of the training data. All LLMs operate in abstracts, using the same manner of informal reasoning as humans do. Even the mistakes they make are amusingly humanlike.
There's no part of an LLM that's called a "mind", but it has a "forward pass", which is quite similar in function. An LLM reasons in small slices - elevating its input text to a highly abstract representation, and then reducing it back down to a token prediction logit, one token at a time.