How do you continue to do your habits even through the toughest days?

Don't be tough on yourself. If life goes sideways, it's better to take a break and begin again tomorrow, than trying to follow your routines no matter what. Just don't tell yourself that if you took a break yesterday, it's ok to take it today too. Yesterday there was a good reason for taking a break, but don't allow that reason to keep you from following your habits, as you'll for sure regret that later.

I try to look at the positive outcomes and how they could make me happier. This is certainly not to say that one should ignore their mental health in any way. If you need that break, take it! And promise to get back on the grind the next day with more energy.