RO-NMO 2010 Problem 72

Let $ABCD$ be a rectangle of centre $O$ , such that $\angle DAC=60^{\circ}$ . The angle bisector of $\angle DAC$ meets $DC$ at $S$ . Lines $OS$ and $AD$ meet at $L$ , and lines $BL$ and $AC$ meet at $M$ . Prove that lines $SM$ and $CL$ are parallel.