how can I output something to the SSMS "Messages" tab from an SSMS add-in

Question

I'm working on an SSMS 2014 addin, and I need to output stuff to the messages tab of the active document.

I know I can get that document like this :

var document = ((DTE2)ServiceCache.ExtensibilityModel).ActiveDocument;

but I've not been able to figure how to access its Messages tab (nor its Results tab for that matter)

Of course, as usual with SSMS Addins, there's no documentation.