Generate a Random Password with Minimum Special Character Requirements in Java

How do I create a random password that meets the system's length and character set requirements in Java?

I have to create a random password that is 10-14 characters long and has at least one uppercase, one lowercase, and one special character. Unfortunately, some special characters are too special and cannot be used, so I cannot use just printed ASCII.

Many of the examples on this site generate a random password or session key without enough entropy in the characters or without realistic requirements in a business setting like the ones given above, so I'm asking more pointed question to get a better answer.

My character set, every special character on a standard US keyboard except for a space:

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A-Z
a-z
0-9
~`!@#$%^&*()-_=+[{]}\|;:'",<.>/?