There are several equivocations involved.
First, it’s not reasoning, but reason that is a requisite of thinking. As Mises puts it, the logical structure of the mind is a requisite for human thinking.
Second, by the term “thinking” Mises is referring to what you have called reasoning. He is not talking about having thoughts in our minds or contemplating certain abstract concepts. He is talking about the process of drawing conclusions about the cause and effect connections in human action.
David Gordon says that creatures who are not human beings may also be able to think even though they lack a human brain. An obvious example is God. But for human beings living in the world, which is the subject matter of economics, a person’s body, including his brain, is a scarce resource.
Indeed, your questions raise philosophical issue that are beyond the scope of praxeology.