Path Integral formulation with a spontaneously broken symmetry?

The path integral evaluates ground state correlation functions, and when a symmetry is spontaneously broken, there are many ground states.

Defining the path integral of a QFT in the naive way, I don’t see any room for there being a degeneracy of the ground state.

How does one determine that a symmetry is spontaneously broken using the path integral formalism? And how do you account for the degeneracy once it’s been determined that a symmetry is broken?