Err, I don't really understand what you would do it that way for.
When you pick up the items, they must change some bool to True, it makes absolutely no difference where this information is at, just that you can get to it. Easiest way is to just stick it on the player since he's the one entering the trigger.
Now that you're getting a bool true on the player, when he enters the trigger just make the trigger Get Fsm Bool on all of the bools you need and do a Bool All True action to see if they're true or not.
If that happens every time the player enters the trigger then you have a fantastic gate system that can decide if the door should open or not. Very simple.