$.$ Please design an engaging memory matching game in Java that incorporates user interaction and tracks gameplay progress. This could include aspects like maintaining game state or recording user scores. Develop at least one core class that manages the game's primary data and logic. This class $($the $$model$)$ should handle the game$$s underlying functions and provide output that can be displayed through a separate interface. If helpful, you may add a draw method to visually render the game on a GraphicsContext. For the interface, use JavaFX to create a graphical user interface $($GUI$)$ that serves as the visual layer of the game. This interface should contain at least three different UI elements, such as Labels, Buttons, Text Fields, or a Canvas. Ensure that the GUI only manages the display and user input; it should call model methods to perform actions and then display the outcomes. Also, customize the style of some elements to enhance the look and feel of the interface.