Weird construction

Geometry Level 4

Given a triangle $$ABC$$ with circumcenter $$O$$, how many moves does it take to draw a line $$\ell$$ through $$O$$ where $$\ell$$ intersects $$AB$$ and $$AC$$ at $$P$$, $$Q$$ such that $$PO=OQ$$?

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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