Cleanup Step, where you discard down to 7 cards, remove all damage from creatures, etc. You don't get priority to play spells or abilities (An exception is Madness) during this step.
You will only get priority if a triggered ability goes on the stack (not just madness, any ability).
And, the clean up step can and will happen over and over again until your handsize is 7. Unless you have a card like spellbook in play, there is no getting around this. If you discard down to 7 and somehow manage to draw cards again, you will then have a new clean up and have to discard again.