  We derive the radial action of a spinning probe particle in Kerr spacetime
from the worldline formalism in the first-order form, focusing on linear in
spin effects. We then develop a novel covariant Dirac bracket formalism to
compute the impulse and the spin kick directly from the radial action,
generalizing some conjectural results in the literature and providing
ready-to-use expressions for amplitude calculations with generic spin
orientations. This allows, for the first time, to find new covariant
expressions for scattering observables in the probe limit up to
$\mathcal{O}(G^6 s_1 s_2^4)$. Finally, we use the action-angle representation
to compute the fundamental frequencies for generic bound orbits, including the
intrinsic spin precession, the periastron advance and the precession of the
orbital plane.
