A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bug moves to its starting vertex on its tenth move is \(m/n,\) where \(m\) and \(n\) are relatively prime positive integers, find \(m + n.\)

(第二十一届AIME2 2003 第13题)