I have been wondering if in my writing the following sentence is grammatically correct:
We accomplish this by first gathering all relevant news stories, then picking out those that mention "bankruptcy", and finally keeping only the ones released by renowned media.
I think it's ok to say by + do-ing but not sure if is fine to use by + do-ing (A) + do-ing (B) + do-ing (C) (can not recall any example). Can anyone tell if this sounds correct? Many thanks!