What am I?

I will try to engage in a Cartesian-styled process of doubt in order to try and uncover what I am speaking about when I say "I" or "me". Descartes made some very provocative inquiries in his Meditations on First Philosophy, however I don't believe he went far enough. When I ask "What am I?", I can feasibly begin with Descartes' "I am a thinking thing" and from there, ask the question "What is it that is thinking?". The statement "I am a thinking thing" is in itself only a thought being presently entertained by the thing that thinks it, presumably me, and cannot be settled on as a definitive answer to the question "What am I?". To understand what I am, I must move past the idea that I am a thinking thing to uncover what it is that is thinking right now. However, I discover a problem here, that is that any answer to the question "What is thinking right now?" or better put perhaps "What is asking this question?", will in itself only be another thought entertained by that which thinks and asks. So I must here ask this: Is an agent a separate entity apart from its action? Is a thinking thing existent apart from its act of thinking? Presumably we would agree that a thing that moves is separate from its motion, that there is the thing, and then there is its motion. But if we take a car, for example, and it is moving, where could we locate its motion as being separate from the car itself? When the car is moving, it is in no way a different object than when it is motionless; so what is its motion? How can we feasibly argue that its motion is distinct from it? But there must be something we can point to that explains the effect motion has on an object, thus proving that motion is indeed a distinct entity. All that we can say here is that there is a change in location. Besides this, motion has no other effect on an object, from the observable viewpoint. And if we point to a moving object at any given moment in time during its motion, as if we were to pause a video of a moving ball, we only see that the ball is in a different place, and that there is nothing present to be called "motion". The confusion encountered here is akin to the question of whether or not a thinking thing can be said to be separate from its thinking. And yet, to say that I am a thinking thing only would be inaccurate, for it is fair to say that I am an eating and drinking thing, a sleeping and walking thing. To say these activities are of the body only and that the Self is distinct from the body is pure speculation, and cannot be shown to be true. However, for now we will operate with the Cartesian foundation of the Self as a thinking thing. Is the thing that thinks separate from its thoughts? I can only answer yes to this question if I can somehow uncover that the thing that thinks is not a thought. Until then, no satisfying answer will ever be given.