While I'm not familiar with ACT directly, I have taken Mindfulness courses (which is what ACT is partially based on). In mindfulness, the practice is to bring as much acceptance, kindness, and gentleness to each moment, and to take good care of yourself. What I like about it is that you don't need to accept something like anxiety or depression as a chronic condition; you just need to accept that at this moment in time, you are suffering, and that you are doing what you can to take care of yourself (whether it be medication, exercise, yoga, acupuncture, or whatever else gives you some peace). It makes sense, because all we really have or know is this moment; we have no idea how we'll feel tomorrow, next week, next month, or next year. It's when we start to worrying or trying to predict how we'll feel tomorrow/next week/next year that we start to spin into those spirals of doubt, anxiety, and depression.
I say this as someone who as an anxiety disorder, and is still working on finding treatment that works. Mindfulness helps but has not been the magic bullet; to be honest, I don't think there is one. But mindfulness helps with perspective.