Actions and frequencies for spinning bodies orbiting Kerr black holes

We compute actions and frequencies for small test bodies with small spins orbiting Kerr black holes. We compute these in closed form in terms of elliptic integrals, using the perturbative integrability of particle motion in the Kerr spacetime. We re-expand our results in the post-Newtonian limit to compare against the integrable 1.5PN system with two spinning bodies.