5.2.4.24 Various problems on the plane

In an angle of size \( 60^{\circ} \) with vertex \( O \) a circle of radius \( 2 \sqrt{3} \) is inscribed, touching the sides of the angle at points \( A \) and \( B \). On the continuation of the segment \( O A \) the point \( A \) is taken to be the point \( P \) so that \( A P=2 \). A straight line is drawn through the point \( P \), intersecting the circle at the points \( M \) and \( N \), and the ray \( O B \) is drawn at the point \( Q \), and \( \quad P M=N Q \). Find the area of ​​the triangle \( O P Q \) if it is known that it does not exceed 27.