On top of pgitu's answer, I also suggest using Parse Anonymous user in which the anonymous user has a field for device ID (the unique identifer for their phone).
Every time the user starts the app, check if a ParseUser is logged in (the anonymous user) if not first check if a user exists with the current device ID for your app and log them in automatically if so. If not, create a new anonymous user and associate the current device id to that new user.
Now, you won't need to force a user signup / login mechanism and you can store information like clicks and such as pgitu suggests. All the remembering of information is done using Parse Anonymous Users and is fairly easy to setup and do.
The catch would be if the user has multiple devices. In this case, you cannot do much with what I'm suggesting but that is just a caveat of having a trial based application and relying on unique devices to mitigate user's and the system. It really shouldn't be an issue though considering you keep track of devices and their # of trials is limited by their # of unique devices.