What is the filter or hook that would allow me to add a custom control (an action link) for admins next to "Edit" on posts on the front end? I want to give admins the option of carrying out an action on a post just as they might click edit while browsing their blog.

I've browsed quite a lot of Google search results and some of the WordPress action listings without identifying what it is I need to use. It may very well be staring me in the face so I would appreciate a nudge in the right direction.

I am, of course, assuming that such a hook/filter exists - if that's not the case is there another approach that I can explore?