How to set iTunes 11 in shuffle or repeat mode via applescript

Question

According to http://dougscripts.com/ setting shuffle and repeat modes via applescript is broken in iTunes 11.

According to this stackoverflow answer shuffle is now a

Answer 1

Spent some time deconstructing all the obfuscated solutions in this post (which appear to not work anymore), here's a more readable and customizable approach that works with iTunes 12.1:

tell application "System Events"

    set itunesMenuBar to process "iTunes"'s first menu bar
    set controlsMenu to itunesMenuBar's menu bar item "Controls"'s first menu
    set shuffleMenu to controlsMenu's menu item "Shuffle"'s first menu

    set shuffleOnMenuItem to shuffleMenu's menu item "On"
    set shuffleSongsMenuItem to shuffleMenu's menu item "Songs"

    tell process "iTunes"
        click shuffleOnMenuItem
        click shuffleSongsMenuItem
    end tell

end tell

This will turn shuffle on and set it to shuffle songs instead of albums, and it should be pretty obvious how to change it to do other things.