  We define P-strict labelings as a generalization of semistandard Young
tableaux and show that promotion on these objects is in equivariant bijection
with a piecewise-linear toggle action on an associated poset, that in many nice
cases is conjugate to rowmotion. We apply this result to flagged tableaux,
Gelfand-Tsetlin patterns, and symplectic tableaux, obtaining new cyclic sieving
and homomesy conjectures. We also show P-strict promotion can be equivalently
defined using Bender-Knuth and jeu de taquin perspectives.
