This is my verbose rambley analysis:
A = A
I am what I am.
What I do is what I do.
My thinking is my thinking.
My knowing is my knowing.
My self-awareness of my own thinking is what I mean when I say I know that I am thinking.
I know that I am thinking because I have self awareness of my thinking.
I know my thinking is my thinking because I know A=A.
I know that I must exist in order to think because I know my thinking presupposes my existence.
I know my thinking presupposes my existence because I cannot think without my thinking being my thinking and that is what I mean by "I exist". I mean that I am what I am or A=A.
A = A
I am what I am.
What I do is what I do.
My thinking is my thinking.
My knowing is my knowing.
My self-awareness of my own thinking is what I mean when I say I know that I am thinking.
I know that I am thinking because I have self awareness of my thinking.
I know my thinking is my thinking because I know A=A.
I know that I must exist in order to think because I know my thinking presupposes my existence.
I know my thinking presupposes my existence because I cannot think without my thinking being my thinking and that is what I mean by "I exist". I mean that I am what I am or A=A.