  We argue that the Sklyanin Poisson bracket on Gr(4,n) can be used to
efficiently test whether an amplitude in planar ${\cal{N}}=4$ supersymmetric
Yang-Mills theory satisfies cluster adjacency. We use this test to show that
cluster adjacency is satisfied by all one- and two-loop MHV amplitudes in this
theory, once suitably regulated. Using this technique we also demonstrate that
cluster adjacency implies the extended Steinmann relations at all particle
multiplicities.
