Starting at \((0,0),\) an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let \(p\) be the probability that the object reaches \((2,2)\) in six or fewer steps. Given that \(p\) can be written in the form \(m/n,\) where \(m\) and \(n\) are relatively prime positive integers, find \(m+n.\)
(第十三届AIME1995 第3题)