Let $AB$ be a chord of a circle with center $O$. Let $C$ be a point on the circle such that $\angle ABC = 30^\circ$ and $O$ lies inside the triangle $ABC$. Let $D$ be a point on $AB$ such that $\angle DCO = \angle OCB = 20^\circ$. Find the measure of $\angle CDO$ in degrees.

Let's think step by step and output the final answer within \boxed{}.
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