When a reminder is triggered give some options for managing this event/task inside the notification drawer. For example options for snooze, postpone or dismiss.

Snooze - remind me later at X minutes/hours/days/weeks
Postpone - reschedule for X min/h/d/w
Dismiss - just swipe the notification away like normally

Also give some custom options so we can modify the X value...

I find this better as a popup screen, because if you are doing something important you dont want to be bothered by and you can attend this later from the notification drawer with more attention...

This comes in handy when you have lots of things and would like to reorganize quickly from the notification drawer without going back into the app.