Two concentric circles have radii \(1\) and \(2\). Two points on the outer circle are chosen independently and uniformly at random. Find the probability that the chord joining the two points intersects the inner circle. Express your answer in the form \(\frac{k}{m}\) where \(\frac{k}{m}\) is a simplified fraction, and give the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
user