Wiring a GFI switch receptacle combo

I asked this question once before and since have new info. I am remodeling a bathroom in a 50 year old house. There was a single light with a pull chain on the ceiling in the bathroom. I removed the fixture (and part of the ceiling) to find the following: two old non-armored wires (appear to be copper) and can't tell which is black or white, coming from the ceiling. There is also another cable with black, white, red and ground wire which looks as though it may be coming from the kitchen. The black and white wires are connected to the two ceiling wires and the red and ground are not connected. From this mess I would like to install a GFI combo with the switch controlling a new light and the receptacle always hot so I can plug something in if necessary. Can this be done with the current setup?? Thanks so much for your help.
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You have to run a three wire cable from this light location to the switch location. Connect the black and white wires from all three cables together, black to black, white to white, connect your new light to the white wires as well. At the GFCI - switch connect the black to the line side, which probably has a bridge connecting two terminals. Connect the neutral to the neutral as indicated on the device, and connect the red to the other side of the switch. Back at the light, connect your other wire from the new fixture to the red. Also connect all ground wires together and to any metal boxes

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