Almost toric neighborhood conjecture for symplectic four-manifolds

Let $(M,\omega)$ be a symplectic four-manifold containing a top-dimensional submanifold with boundary that is diffeomorphic to an almost toric manifold whose base has a one-stratum diffeomorphic to an interval. Almost toric neighborhood conjecture. Then $(M,\omega)$ contains an almost toric submanifold with boundary diffeomorphic to and contained in the given one. This would generalize the fact that chains of symplectic surfaces have toric neighborhoods and could provide a method for finding embedded lens spaces with toric neighborhoods for generalized almost toric surgeries.