I'm sure this would be implemented as a trigger event, but there is no such event, so I surmise there isn't one.
Failing that, I searched the wiki for reminder, notification, alarm, and even bulletin, but none were successful.
So, Vasiliy, I propose a new trigger event, maybe called Upon receipt of a reminder, optionally with the DateTime field value or name as a read-only argument or made available to the script in any other fashion. I'd love hear your comments on this, but I know you are a very busy person.