A triangle $\triangle ABC$ is situated on the plane and a point $E$ is given on segment $AC$. Let $D$ be a point in the plane such that lines $AD$ and $BE$ are parallel. Suppose that $\angle EBC = 25^\circ$, $\angle BCA = 32^\circ$, and $\angle CAB = 60^\circ$. Find the smallest possible value of $\angle DAB$ in degrees.

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