  We show that every (possibly degenerate) contact form on a closed
three-manifold has at least two embedded Reeb orbits. We also show that if
there are only finitely many embedded Reeb orbits, then their symplectic
actions are not all integer multiples of a single real number; and if there are
exactly two embedded Reeb orbits, then the product of their symplectic actions
is less than or equal to the contact volume of the manifold. The proofs use a
relation between the contact volume and the asymptotics of the amount of
symplectic action needed to represent certain classes in embedded contact
homology, recently proved by the authors and V. Ramos.
