[dragon96]

Regardless of which text you choose, I recommend writing proofs (full sentences and all) for the solutions that were harder to come by, or you feel difficulty expressing clearly. And if you can, get some feedback on the proofs. (Happy to take a look at a few if you DM me)

The process of writing will hopefully help you:

  - build awareness of when your arguments are not airtight or when you make false assumptions
  - modularize your thinking 
  - become more fluent with logical "vocabulary"

As for books, my personal favorites were Problem Solving Strategies (Engel) and Art and Craft of Problem Solving (Zeitz). They're both really approachable, have plenty of examples, and will give you a different perspective on what math can be about.