Composition in Java

I'm having a hard time implementing a simple composition example in Java:

Java Code:

public class CompositionPattern {

        public static void main(String[] args) {
                Udp udp = new Udp();
                Imap imap = new Imap();
                udp.startService();
                imap.startService();
        }

}

public class Imap {
        private Responder responder;
        
        public Imap(){
                this.responder = new Responder(this);
        }
        
        public void startService(){
                responder.doStuff();
        }
        
        public boolean supportsMe(){
                return true;
        }
}

public class Udp {
        private Responder responder;
        
        public Udp(){
                this.responder = new Responder(this);
        }
        
        public void startService(){
                responder.doStuff();
        }
        
        public boolean supportsMe(){
                return false;
        }
}

public class Responder {
        Object parent;
        
        public Responder(Object parent){
                this.parent = parent;
        }
        
        public void doStuff(){
                if(parent.supportsMe()){
                        System.out.println("Parent supports me.");
                } else {
                        System.out.println("Parent doesn't support me.");
                }
        }
}

The above won't compile. It says "The method supportsMe() is undefined for the type Object". I understand that I stored parent as an Object. But in reality it is not simply Object, but a Udp object or Imap object. The point is to make Responder generic. I don't want to have to cast the Object to Udp or Imap. Any solutions so I can keep this generic?