I think, therefore I am is the simplest and truest statement of the false, or ego self. That thought begets all other self thoughts. Your whole identity is wrapped up in subsequent thoughts.
The "I" thought has taken over. Therefore you you believe, "I think therefore I am." This is a false identity. You are prior to the "I" thought.
I am, therefore I think, is truer. At least it points to the "I am" that is prior to thought. Beingnes is multitude. And that's OK. But the truth is prior to the multitude that believes it is.
All bodies have a sense of beingness, of I amness. But, did any body create this sense? Did you create your own beingness as an individual? Or, did beingness arrive, unbidden, to take you for a drive? Take a look. Are you the driver? Or are you driven.
When the beingness arrived, it took a couple years for the mind to develop. At around two or three, the conceptual mind found it's first foothold as "I." The rest is a house of cards. The whole you that you think you are is based on this first "I" thought.
You have to go back to the original "I" thought and back track from there. The "I" thought is the result of Being in a body. You are the Beingness that created the body.
You can only think your way out of this by coming to the end of thought. Or, one might say, when thinking is no longer satisfactory, and sees its own limitation, perhaps there will just be seeing/knowing, without a thinker, without a you.