Let $P$ and $Q$ be points on $AC$ and $AB$, respectively, of triangle $\triangle ABC$ such that $PB=PC$ and $PQ \perp AB$. Suppose $\frac{AQ}{QB}=\frac{AP}{PB}$. Find $\angle CBA$, in degrees.

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