If we suppose that we don’t have free will, then we can’t say that we’ve reached this conclusion by reason. For to reason requires engaging in a mindful task that is not reducible to unreasoning matter. However, if we are in fact determined, then it follows that everything we do is caused by something external to us which is perfectly unreasoning.
If everything we do is caused by unreasoning matter, then it follows that everything we’re doing is unreasoning. This would include our illusory “reasoning” that concluded that we are determined.
Therefore, we are not determined; we have free will. Free will is necessary to reason.