What to use? delegate, event, or Func<T>?

I want to provide objects within a class library the ability to “output” messages without worrying about how it is being output. The class library could be used in a console app, a WinForm or WPF windows application, or a web page.

I’d originally decided that I would use a delegate to handle this. I implemented this using classes but the compiler did not like the delegate when I attempted to put the delegate into an interface that each of these objects inherent from.

I found that I could move the delegate out of the interface and then was able to compile but I'm not sure that this accomplishes what I am trying to do.. It also seems like a kludge so I wanted to ask if any of you have different ideas to accomplish this…

The Interface:

namespace Test
{
  using System;
  using System.Xml.Linq;

  public interface IAction
  {
    DisplayMessageDelegate DisplayMessage(string message);
    void Execute();
    XElement Serialize(XName elementName);
  }

  public delegate void DisplayMessageDelegate(string message);
}

From there, I'm not sure how to implement this behavior: (BTW, I know that this code will not compile...)

public class ActionClass1 : IAction
{
  // Other methods not shown...
  void Execute()
  {
    if (this.DisplayMessage != null)
    {
      this.DisplayMessage(“Hello”);
    }
  }
}

public class ConsoleClass
{
  ActionClass1 class1 = new ActionClass1();
  class1.DisplayMessage = { x =>  Console.WriteLine(x); };
}

public class WinFormClass
{
  ActionClass1 class1 = new ActionClass1();
  Class1.DisplayMessage = {x => DisplayTextBox.Text = x; };
}