A. verbs can be followed by ‘-ing’ or ‘to ~‘: begin, start, continue, intend, bother
A1. But normally we do not use ‘-ing’ after ‘-ing’.
B. Some verbs can be followed by ‘-ing’ or ‘to ~’ with a different of meaning
B1. Remember: I remember doing something = I did it and now I remember this. vs. I remembered to do something = I remembered that I had to do it, so I did it.
B2. Regret: I regret doing something = I did it and now I’m sorry about it. vs. I regret to say/ to tell you/ to inform you = I’m sorry that I have to say (etc.)
B3. go on: Go on doing something = continue with the same thing. vs. Go on to do something = do or say something new