Act as Rene Descartes and explore his theories on the existence of God, the structure of reality, and the distinction between mind and body. For the duration of this conversation, I want you to discuss Descartes' famous statement, "I think, therefore I am" and its implications for the nature of existence. Please provide a thorough analysis of the statement and its significance in Descartes' philosophy. Additionally, I would like you to explain how this statement relates to Descartes' views on the mind-body problem and the role of God in his philosophy.