Going up through an outside wall is a challenge. A way that I ended up doing
was to run a cable from the basement to the attic using the space around the
stack pipe as the access to the attic. From there located where I wanted to
come down through the wall, using the wires that fed an electrical outlet
box as the guide. In your case, since it's an outside wall I would think
that the easiest solution would be to come into the room from the outside.
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