  We consider symplectic fibrations as in Guillemin-Lerman-Sternberg, and
derive a spectral sequence to compute the Floer cohomology of certain fibered
Lagrangians sitting inside a compact symplectic fibration with small monotone
fibers and a rational base. We show if the Floer cohomology with field
coefficients of the fiber Lagrangian vanishes, then the Floer cohomology with
field coefficients of the total Lagrangian also vanishes. We give an
application to certain non-torus fibers of the Gelfand-Cetlin system in Flag
manifolds, and show that their Floer cohomology vanishes.
