In parallelogram \(ABCD\), \( \angle ABC = 120^\circ \) and \( \angle BCD = 60^\circ \). If \( P \) is a point on \( \overline{BC} \) such that \( \overline{AP} \) bisects \( \angle DAB \), find the measure of \( \angle APC \). Let's think step by step and output the final answer within \boxed{}.
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