replied on October 30, 2014
Hey Justin,
I think there may have been some confusion. In my original response, I said...
"The builtin Workflow activities won't close the document viewer, but once the business process runs, you can close the window manually."
(If this isn't what you originally saw, I edited my post after I got some feedback from a developer that stated that Workflow cannot close the document viewer on another specific user's computer).
The general idea is that you can have an "approved" business process button that contains a "assign field values" activity whose sole purpose is to update the metadata from pending to approved. You can have the alternate business process with the same set up, except it assigns the field to denied.
If closing the document viewer automatically is a necessary step, you may be able to get around this entirely by checking out the document preview pane. This allows you to see the document/metadata/thumbnails of a document without actually having to open it. This way you can run the business process from the client and never have to worry about closing the document viewer for approved or rejected documents.