Exactly! Thinking, by the way, is just the common term for reasoning. Logic is the formailzation of correct reason. Therefore, all thought is "reasoning," that is, the use of the rational faculty (since it is the only one we have to think with). I think part of the problem here, is a misunderstanding of what rationality actually means. It does not mean reasoning correctly, it means only the capacity to reason or the faculty with which we reason. It can be used both correctly and incorrectly.
Hank