A data science team is trying to speed up their Python script by using the threading module to process multiple large data files at once on a multi-core machine. They are surprised to observe no significant performance improvement. Please explain the following:

1. What is the Global Interpreter Lock (GIL)? Describe its purpose and how it functions in CPython.
2. Why does the GIL prevent true parallelism when using the threading module for CPU-bound tasks (like processing large data files) on multi-core machines, leading to the team's observed lack of performance improvement?
3. Suggest an alternative solution that would allow for true parallelism in this scenario. Specifically mention the multiprocessing module.
4. Explain how the suggested alternative (multiprocessing) overcomes the limitations of the GIL to achieve actual speedup on multi-core systems for CPU-bound tasks. Compare and contrast its execution model with threading.