We provide a combinatorial way to locate non-displaceable Lagrangian toric fibers on
any compact toric manifold. By taking the intersection of certain tropicalizations coming from its
moment polytope, one can detect all Lagrangian toric fibers having non-vanishing Floer cohomology
([15, 16]). The intersection completely characterizes all non-displaceable toric fibers in some cases
including pseudo symmetric smooth Fano varieties ([13])