$\left[\begin{array}{l}{[\text { Ratio of areas of triangles with a common angle }} \\ {\left[\begin{array}{l}\text { Law of Cosines }\end{array}\right]}\end{array}\right.$

In triangle $A B C$, angle $A$ is $60^{\circ} ; A B: A C=3: 2$. Points $M$ and $N$ are located on sides $A B$ and $A C$ respectively, such that $B M=M N=N C$. Find the ratio of the area of triangle $A M N$ to the area of triangle $A B C$.