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regex - Regular Expression to match a valid day in a date

I need help coming up with a regex to make sure the user enters a valid date The string will be in the format of mm/dd/yyyy

Here is what I have come up with so far.

/[1-9]|0[1-9]|1[0-2]/d{1,2}/19|20dd/

I have validated the regex where the user cannot enter a day higher than 12 and the years have to start with either "19" or "20". What I am having trouble is figuring out some logic for validating the day. The day should not go over 31.

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Regex for 0-31:

(0[1-9]|[12]d|3[01])

Or if you don't want days with a preceding zero (e.g. 05):

([1-9]|[12]d|3[01])

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