What I don't understand is that the act of observing your own thoughts is still a thoughtful action.
If thinking is like inner speech, then there is also an option to be quiet for a while. You start the act of observation by telling yourself "now I am going to observe", but then you can stop talking.
The goal is not to stop thinking forever. Thoughts are useful. The goal is to stop thinking obsessively.
Thinking is like drawing pictures, and watching those pictures is a different process.