iTerm2 + tmux switch window shortcuts

I use CMD+Shift+{} as a default tab switching shortcuts across many applications (browsers, code editors, etc.).
So I decided to add following to my iTerm2 config:

As I use iTerm2 with tmux and tmux windows is like tabs for me, so I want to switch them with the same shortcuts.

I added key binding with "Send text" command for that.

For next window use:

tmux next-window \n

For prev window use:

tmux previous-window \n

You can use it even for cycling through windows back and forward.

If you know the way how to avoid actually printing these commands in console please let me know.