In text, does 'enumerate' imply a numbered list?
Solution 1:
From Merriam Webster’s page on enumerate:
1: to ascertain the number of: Count
2: to specify one after another: List
Also from Merriam Webster’s page on enumerate
Despite its numer- root, you don't have to use numbers when enumerating.
Based on the information provided by the dictionary’s page on the word, I can only conclude that you can enumerate your reasons without using numbers or giving the impression that you’re relying on a numbered list.
I would urge you to take a look at the Merriam Webster’s page on the said word.