I always saw I think therefore I am as a definition of to be. What it basically says is that "Thought exists" and that when you are referring to yourself, ultimately, you are referring to these thoughts that you are certain exist. When you say "I walk", you mean "those thoughts of which I am certain perceive, through senses, that they are attached to a body that is walking".

It also means that those thoughts of which you are not certain, such as "we must allow the use of brains to think about thinking" are not part of you; they are a separate object. You are the presence of this thought, not its result.