It keeps telling me INPUT isn't recognized in the FileProcessor class.
Please use Java naming conventions ie don't use all upper case letters for variable names unless they are constants.

The problem is INPUT is a parameter in the doInBackground classes constructor and not a instance variable and so it is not visible in the doInBackground() method. In the constructor assign INPUT to an instance variable and use that to refer to the file.

How would I get counter in FileProcessor to constantly update to outerTextArea in class X?
You provide an implementation of the process(..) method to update the text area and call publish(..) from the doInBackground() to pass the data to display to the process() method.