Why do we brush, then floss our teeth?

Most of the cavities I've had, is in between my teeth, and then I got thinking, why do we brush then floss our teeth?

If there's something in between the teeth, and you brush, you won't get between the teeth, and then you floss, and so it's still dirty.

Why not floss then brush your teeth? Does this make sense to anyone else?
Why do we brush, then floss our teeth?
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