Please reason step by step, and put your final answer within \boxed{}.
Given a cyclic quadrilateral \( ABCD \). Rays \( AB \) and \( DC \) intersect at point \( K \). It turns out that points \( B \), \( D \), and the midpoints \( M \) and \( N \) of segments \( AC \) and \( KC \) lie on the same circle. What values can the angle \( ADC \) take?
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