Abstract: Given Lagrangians in a symplectic manifold M, we prove the quilted Floer cochain complexes and tensor products of Floer cochain complexes form (A_infity, n) modules over a subcategory of the Fukaya category Fuk(M times M^-) generated by product Lagrangians and graphs. As an application we prove two long exact sequences conjectured by Seidel that relates the Lagrangian Floer cohomology of a collection of (possibly intersecting) Lagrangian spheres {L_i} and the fixed point Floer cohomology of composed Dehn twists tau_{L_1} \circ \cdots tau_{L_n} along them.