I think there's a strong argument to be made that the answer to this question depends on exactly what you mean by "reason" and "predict".

If you mean "predict" in the same sense as it's used in the phrase "predictive model", then the answer could be a resounding no - there's a hypothesis that the brain implements just one basic learning algorithm, and everything else is just emergent phenomena coming out of that.

I think there is a difference, but my view is that it is impossible to reason without sufficiently accurate prediction, and that the concepts we use for reasoning are largely formed based on how predictive they are. Consider playing a game where two players throw dice, and the one with the larger number wins. There is no predictability between turns, so there is no point in reasoning far into the future, unlike in chess, where the positions change slowly, one piece per turn and in predictable patterns. In chess you still don't know what the other player will do, but you can reason about it, because there is a level of predictability.

I would define reasoning as answering a question or optimization problem, e.g. What is my best move? What is a good move? This can be formalized as calculating some kind of score for a possible action, whereas prediction is just about assigning a probability value to an event.