OPM 2023 Problem 4

Let $[ABC]$ be an equilateral triangle and $P$ be a point on $AC$ such that $\overline{PC}= 7$ . The straight line that passes through $P$ and is perpendicular to $AC$ , intersects $CB$ at point $M$ and intersects $AB$ at point $Q$ . The midpoint $N$ of $[MQ]$ is such that $\overline{BN} = 14$ . Determine the side of the triangle $[ABC]$ .