Blessed Angle Bisectors

Let $ABC$ be a scalene triangle with $\angle A = 60^\circ$ .

Let $BF$ and $CE$ be the angle bisectors of angles $B$ and $C$ , respectively, with $E$ and $F$ on $AB$ and $AC$ , respectively.

Let $AP$ be perpendicular to $EF$ at $P$ . Extend $AP$ to meet $BC$ at $M$ .

Find the ratio $AP : PM$ .

Give your answer to 2 decimal places.