Two lines and a point

Level pending

Two parallel lines, $$m$$ and $$n$$, and a point $$P$$, are given, where $$P$$ does not lie between the lines. The distance from $$P$$ to $$m$$ is double the distance from $$P$$ to $$n$$. How many uses of a straightedge and compass does it take to draw a line through $$P$$ perpendicular to $$m$$ and $$n$$?

All terminology in this question is explained in the first note of my straightedge and compass set. More straightedge and compass constructions can be found there.

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