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Now to start debugging the code. I added a toString() method to the ListNode class so it can be printed easily. Print out the value and the next. A side effect is it will print the whole list thru...

It's missing the ListNode class definition.

How would I compile and test the program?

You should not need a try/catch block for an event that the program should never let happen.
Can you post code that compiles, executes and shows the problem?