Problem

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Let $ABCD$ be a convex quadrilateral such that $\angle ADC=\angle BCD>90^{\circ}$. Let $E$ be the point of intersection of $AC$ and the line through $B$ parallel to $AD;$ let $F$ be the point of intersection of $BD$ and the line through $A$ parallel to $BC.$ Prove that $EF\parallel CD.$