A bug walks all day and sleeps all night. On the first day, it starts at point O, faces east, and walks a distance of 5 units due east. Each night the bug rotates 60^{\circ} counterclockwise. Each day it walks in this new direction half as far as it walked the previous day. The bug gets arbitrarily close to point P. Then O P^{2}=\frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.