Markov Chains & Long-Run Behavior · Medium problem

A chain on states 1, 2, 3 moves as follows. From state 1 it moves to state 2 with probability $1/2$ and otherwise stays at 1. From state 2 it moves to state 1, stays at 2, or moves to state 3, each with probability $1/3$. State 3 is absorbing. Starting in state 1, what is the expected number of steps until the chain reaches state 3?