Two moons, Moon X and Moon Y, are separated by a center-to-center distance \(R\). The magnitude of the gravitational force that Moon X exerts on Moon Y is \(F\). Moon X then collides with a large asteroid, which causes Moon X to double its mass. Due to the collision, the orbital path is altered such that the center-to-center distance between the two moons is reduced to \(\dfrac{1}{2}R\). If the mass of Moon Y remains constant, what is the new magnitude of the gravitational force that Moon X exerts on Moon Y?