Defining an abstract method in enum

In Java you can define abstract methods for an enum type to override it with a concrete method in a constant-specific class body (see Effective Java, 2nd Ed., page 152). When I try to do the same in Groovy I get a compilation error:

Can't have an abstract method in a non-abstract class. The class 'Day' must be declared abstract or the method 'java.lang.String getAction()' must be implemented.

This compilation error can be reproduced with this enum:

enum Day {
   SUNDAY {
      String getAction() {
         'Relax'
      }
   },
   MONDAY {
       String getAction() {
          'Work'
       }
   }

   abstract String getAction()
}

An enum in Groovy should provide the same behavior for enums as Java.