$P$-strict promotion and $B$-bounded rowmotion, with applications to tableaux of many flavors

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