$\left[\begin{array}{l}{[\text { Similar auxiliary triangles }} \\ {[\text { Properties and characteristics of a parallelogram }]}\end{array}\right]$

Points $M$ and $N$ are the midpoints of sides $B C$ and $C D$ of parallelogram $A B C D$, respectively. Segments $A M$ and $B N$ intersect at point $O$.

Find the ratio $M O: O A$.