How can one relate Buddhism epistemology of Thought and Attention to its Western counterpart? There are at least two possibilities, and no doubt many more besides.

The first one turns around the Cartesian dictum, "Cogito ergo sum", "I think therefore I am".  René Descartes got off to a brilliant start and then promptly took a wrong turn, completely missing the point of his inadvertent discovery.

He turned right, taking the very 'doubt' that he took as evidence of his 'existence', making it the keystone of his entire intellectual edifice.  Instead, he should have turned left and investigated it.  So as to realise it's causal factors, thereby realising it's true nature, "... thus I am simply the result of that thought". 

The second possibility considers the two Grail Legend questions.  "What does it mean?" and, "Whom does it serve?"  The first investigates the object of attention.  The second investigates the subject himself, using the same principles, in the same way, to find the same answer.

One could also think of a teaching given to Carlos Castaneda, Don Juan's "second attention": though others might not agree.
I. "I think therefore I am". In Buddhist and Hindu Meditation, thought is simply one more aspect of samsara. Thought is ultimately realized to be a hindrance. The goal is to "go" beyond thought and beyond no thought to one's "natural self" (Hinduism) or "dharmakaya" (Buddhism). One realizes the ultimate truth. (I.e., thinking is part of awareness. In meditation, moving past awareness into realizing one's natural self, or dharmakaya, is possible.) (There is something past or beyond "thought and no thought". There are (seem to be) many alive today in that state of Liberation. )

So, your statement, " I am simply the result of that thought", does make sense. No thought, no "I", but something is still there. Meditation helps you learn what that is/you are.

II. Different strokes, etc. This question actually divides certain Tibetan Schools of Buddhism. Well, seems to. It's more like there seem to be many Buddhist Traditions, and "schools" within those traditions. If everyone thought the same way, only one tradition, indeed only one religion would be needed. My experience has shown me that I am the type that prefers to investigate the subject, "me", as I seem to have more success in that type of meditation. (And don't get me started on Carlos Castenada. I was so disappointed that his books turned out to be fiction. Never read another word after that revelation. Was a fun read up to then, though.)