I'm working off of Kant's conception of analytic/synthetic and a prior/a posteriori judgements.
The definition of "thoughts" does not subsume their existence. That is, it is logically possible to talk about thoughts in a world where humans are not around to think them. Therefore, "thoughts exist" is not true by the definition of what a "thought" is, and hence not analytic, but rather synthetic.
However, the fact that I am here right now having thoughts means that their existence is necessarily true. I do not need to go outside and look at the sky to confirm this, nor go to the library and read a book to confirm this. The fact that I had a thought necessitates their existence.