Lily pads $1,2,3,\dots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$. From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen randomly with probability $\frac{1}{2}$ and independently of other jumps. The probability that the frog visits pad $7$ is $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.