>>17780418grammatically? it's fine. if I added a few more words, does it make more sense?
"I can't stop [whatever I'm doing] to cry. I need to keep going.
replacing 'to' with 'and' makes it a sequence of events while using 'to' indicates the purpose of stopping is to cry.
two similar sentences are:
"In cities people won't stop [walking] to help someone."
"Your dad can't stop drinking to save his marriage."
there is a potential second meaning of the sentences, but it usually makes no sense. Why would walking help someone? Drinking to save a marriage? Huh?