“I Think, therefore I Am” statement is misleading. Let me explain my perspective on it.
When you were a child, you still were there, but there was no thinking. When you meditate you don’t think, but you are still there. So the idea that you exist only because of your thoughts is not true.
This statement says that your thoughts are your whole world. You stop thinking and you don’t exist. This is so not true. Even a person who has some sort of mental disability is still present and alive. Even when someone looses their memory, they still are.
One thing we are doing wrong in this age is that we have given too much importance to our thoughts. Though all your best moments happened when you were not actively thinking, somehow thoughts are given more prominence.
Here’s how I would rephrase it “I Am, therefore I think”