Let A B C be a triangle where M is the midpoint of \overline{A C}, and \overline{C N} is the angle bisector of \angle A C B with N on \overline{A B}. Let X be the intersection of the median \overline{B M} and the bisector \overline{C N}. In addition \triangle B X N is equilateral and A C=2. What is B N^{2} ?
Answer Choices
A. \dfrac{10-6 \sqrt{2}}{7}
B. \dfrac{2}{9}
C. \dfrac{5 \sqrt{2}-3 \sqrt{3}}{8}
D. \dfrac{\sqrt{2}}{6}
E. \dfrac{3 \sqrt{3}-4}{5}