Adding Artboard actions to an Action?

Here's what I want the action to do:

Clear the selected object

Fit the Artboard to the Selected Object

Save for Web and Devices

I can get it to clear and save but I'll be darned if I can get the Fit the Artboard to the Selected Object to register in the recording of the action.  No matter what shortcuts I use, menues I use it just won't record it.  Is this just a thing Illustrator won't do or any I just missing something?

I do those 3 things listed above ALL the time and it would be nice it I could make those 3 things into 1 action, then add that action to a hot key on my tablet.

Thanks.