"State" is a good, plain, ordinary word. It is used frequently. When you "state" an idea, the idea is usually precise and factual. To "state" it means to express a thought it carefully, clearly, and in a formal way. It is a declaration a belief for the record.
"Would you agree that the accident was your fault?'
"No, I wouldn't."
"But when you talked to the police you stated 'I was driving behind him, a cat ran out in front of his car, and he stopped so suddenly that I couldn't stop in time and hit his car.'"
"Verbalize" is a less common word. To "verbalize" an idea means that the idea is difficult to express in words, but you have found a way to do it.
"It is hard to verbalize exactly what it is about Irving Berlin's songs that makes them such a joy to listen to."