Sonya the frog chooses a point uniformly at random lying within the square $[0,5]\times [0,5]$ in the coordinate plane and hops to that point. She then randomly chooses a distance uniformly at random from $[0,0.5]$ and a direction uniformly at random from $\text{north, south, east, west}$. All her choices are independent. She now hops the distance in the chosen direction. What is the probability that she lands outside the square?