I am in the process of remodeling an older bathroom (1965) and had a question regarding the wiring.
From the single switch box where the feed from the circuit breaker comes in there is a 12/3 circuit going to the ceiling fan/light. There is also a 12/2 going to the vanity light. Can I change the 12/2 to a 12/3 and take the unswitched 2nd hot and the shared common and ground and run a 12/2 from the vanity light box to a GFI outlet. The reason I'd like to do it this way is because the single switch box is going to be pretty crowded if I run an additional 12/2 for the single outlet.

