Deriving force acting on magnetic dipoles using the Lorentz force

I was always taught that classically all electromagnetic phenomena are encapsulated in the Maxwell equations and the Lorentz force formula for point charges:
$$ vec{F} = qleft(vec{E}+vec{v} times vec{B}right)$$
but according to this equation the magnetic field doesn’t do any work. So I have two seeming contradictions in mind that I can’t explain:

1. I don’t see how this formula can explain the energy a magnetic dipole has in a magnetic field:
   $$U=-mathbf{m} cdot mathbf{B}$$
   According to the formula there should in no way be a generating potential for any magnetic force. And furthermore that dipole energy formula implies that the magnetic field can in fact accelerate and do work, no?
2. Also a phenomena that everyone observes with their own eyes: When you bring two permanent magnets together at some point they will snap together, accelerating and acquiring kinetic energy in the process. This is again seemingly the magnetic field doing work which isn’t allowed by the Lorentz force.

How does one resolve all this?