It seems as if most have missed the purity of the thought. The thought incorporates the entirty of the person, the individual the “ I“ and inclusive of the thought itself which gives it it's consciousness It is the validation and verification of self unto itself, and needs no other validation nor verification.
To put another way...
The thought say unto itself “ I am thinking about the thought that I am thinking, thus the thought that I am thinking exist unto me.... Thus I am.
The thought cannot be applied to a group as a collective, because there must first be the collective agreement among the individuals of the group.
When there is unity the collective become singular and the “I“applies. “We think therefore we are“ isn't applicable in every situation, because the we must be first unified by full agreement...and in such a situation it can easily be substituted with I, to show solidarity in their unification.
I is the consciousness of the thought of itself. Am it the awareness of its own existence.