Is it advisable to call abstract methods from a method in that Abstract Class

I have been wondering about this for a long time.

I have to perform this process -

process(){
   bool allow=checkForPermission();
   if(allow) {
      processRequest();
   }
   sendResponse();
}

Now I have made an abstract Class X with three abstract methods:

abstract class X {
   public abstract sendResponse();
   public abstract checkPermission();
   public abstract sendResponse();
   public abstract example(); // some example which is called from sendResponse() from where it is implemented.

   public void process() {
      bool allow=checkForPermission();
      if(allow) {
         processRequest();
      }
      sendResponse();
   }
}

Class A extends X; this is where I am uncertain. When A is implementing all the abstract methods, and in sendResponse() method it is making a call to IfError() Function, is it a good design?

My friend suggests this: Its like compiler will first call X.process() then to A implemented methods, and again A to X (where sendResponse() will call example() method), which my friend said is not a good design:

X obj = new A();
obj.process();

Will it be a good design?