Single Threading - GUI Scripting

I want to call an MacOS application from Hazel but I can only use AppleScript GUI scripting for that application (i.e. it doesn't support native scripting ... grrr).
I want Hazel to call the application once for each file. I've written the AppleScript to call the app via its GUI and it works fine.
My question is:
How can I guarantee that Hazel is only going to execute the rules serially when they match my file criteria? If Hazel noticed that there were three files that met the criteria, I wouldn't want Hazel launching three instances of my AppleScript at the same time. Since, if there's a single instance of the other application, I should only be simulating one set of button and menu clicks at a time.
Many thanks indeed in advance.
I want Hazel to call the application once for each file. I've written the AppleScript to call the app via its GUI and it works fine.
My question is:
How can I guarantee that Hazel is only going to execute the rules serially when they match my file criteria? If Hazel noticed that there were three files that met the criteria, I wouldn't want Hazel launching three instances of my AppleScript at the same time. Since, if there's a single instance of the other application, I should only be simulating one set of button and menu clicks at a time.
Many thanks indeed in advance.