Can someone explain how to wire a bathroom fan using the wiring from a standard outlet? Attached is a photo of the outlet's wiring.

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I believe the clump of white wires together is neutral and the black is hot. There are also a blue, red, and another white that connect in the box that I believe are for rooms above this 1/2 bath.

I plan on running the wiring behind a chair rail molding around the room to its own switch.
I thought of wiring it straight to an overhead light in this room, but I rather have it work with its own switch and not turn on with the light...

The fan is a simple duct-less Broan that has a black and a white wire. No light, warmer, etc.

Any advice is appreciated.