Expected Value, Linearity & Advanced Probability · Superchallenge problem

A token starts at position $1$ on $\{0,1,2,3\}$. Each step it moves right with probability $\tfrac23$ and left with probability $\tfrac13$, stopping at $0$ or $3$. Find the expected number of steps until it stops.

The answer is a fraction $\tfrac{m}{n}$ in lowest terms; find $m + n$.