Applescript to reboot router by clicking on buttons
There's no way for me to know if this following code will help you, without being able to see the website and test the script.  The action for clicking a button in Safari (by identifying the button by its ID), requires the use of JavaScript within your AppleScript code…

As long as this button is not within a drop-down menu or pop-up window or something else, this script should work for you

tell application "Safari"
    do JavaScript "document.getElementById('menu_tools').click();" in document 1
end tell