I’m afraid that the verb phrase “put together” can mean a few different things.
1. “Assemble” - (Verb) as you mentioned; EX. “Yesterday, I put together the baby’s bassinet.”
2. “Draft” or “Write” - (Verb) EX. “Put together an essay about your opinion about gun control laws.”
3. “Well dressed”- (Adjective) EX. “Jenna always looks put together.”
These are the three that I could think of off of the top of my head. Let me know if you need any further clarification! I hope this helps!