The Cogito (n.) looks like a perfect circle only because it hides the distance: the doubt that returns is already past.
The Cogito (n.) does not describe the birth of the subject; the one who doubts has to exist before the doubt begins.
The Cogito (n.) proves nothing, Lamennais claimed: saying 'I think' is just saying 'I am thinking', assuming what it wants to prove.
The Cogito (n.) is a sentence whose truth is the act of saying it: it states nothing but that act, so it proves itself by functioning.
The Cogito (n.) is a loop in which truth and reality build each other: the proposition is a real truth, and the act of thinking it a true reality.
The Cogito (n.) is the rare case where one act is caught as both a thing and a doing; the harder you doubt it as an object, the more it stands up as something you cannot doubt.