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2 Made the question a bit more open

Suppose that $M$ is a symplectic manifold with a Hamiltonian circle action. Is there a topological Lefschetz pencil on $M$, $f\colon M-A \rightarrow S^2$, such that the fibers are symplectic submanifolds of $M$ and such that the circle action restricts to a Hamiltonian circle action on the fibers?

Suppose that $M$ is a symplectic manifold with a Hamiltonian circle action. Is there a topological Lefschetz pencil on $M$, $f\colon M-A \rightarrow S^2$, such that the fibers are symplectic submanifolds of $M$ and such that the circle action restricts to a Hamiltonian circle action on the fibers?