Is it possible to create a Jbutton with both an ActionListener and MouseListener

Meaning so i create a button and then when i press it ( throught actionListener) it changes the frame so that AFTER then button was pressed i can press anywhere on the frame and MouseListener would in use.

JButton button = new JButton();//Creates Button
button.addActionListener(new ActionListener() {         
public void actionPerformed(ActionEvent e) {
    //Insert MouseListener
    //Then do something with mouseListener
}
}); 

Heres the curent code: however they're now in sync when i try to click the button and i cannot call mouseListener a 2nd time

    JButton button2 = new JButton("Click");
    button2.addActionListener(new ActionListener()
    {
        public void actionPerformed(ActionEvent e)
        {
            System.out.println("You clicked the button");
            newCube.stopCube();
        }

    });
    button2.addMouseListener(new java.awt.event.MouseAdapter()
    {
        public void mousePressed(java.awt.event.MouseEvent evt)
        {
            double x = evt.getX();
            double y = evt.getY();
            newCube.setCube(x,y);
        }
    });