I’ll save you the headaches and suggest that unless you are a programmer with a degree, or with a few years experience or have someone to mentor you on this it is not a path to take. I only noted it for others that would read this.
You may find the Chain of Thought prompting is enough to improve your results. I don’t plan to check it out for your case but if I were tutoring someone would take the time.
FYI for others
Update (12/08/2023)
You might find my reply of interest. I would not expect the same level of result with code using constraints but if you find success let me know.