, 2005

A goat starts at the origin $(0,0)$ and then makes several moves. On move 1, it travels 1 unit up to $(0,1)$. On move 2, it travels 2 units right to $(2,1)$. On move 3, it travels 3 units down to $(2,-2)$. On move 4, it travels 4 units to $(-2,-2)$. It continues in this fashion, so that on move $n$, it turns $90^\circ$ in a clockwise direction from its previous heading and travels $n$ units in this new direction. After $n$ moves, the goat has travelled a total of 55 units. Determine the coordinates of its position at this time.