Need help creating a new keymap

[svban]

I am on MacOs. I want to create a keymap, that on press

1. If firefox not running -> open it.
2. If firefox running, but not active -> activate it.
3. If firefox running, and active -> cycle through all the open firefox windows.

I've tried implementing this with applescript, but it is not working with skhd for some reason. Only 1 and 2 is working, but 3 is not working for some reason.

skhdrc

alt - f : $HOME/firefox.sh

firefox.sh

osascript -e '
tell application "System Events" to set appList to name of processes
if "Firefox" is not in appList then
    do shell script "open -a Firefox"
else
    tell application "Firefox"
        if frontmost then
            tell application "System Events"
                keystroke "`" using {command down}
            end tell
        else
            activate
        end if
    end tell
end if'