Markov Chains & Long-Run Behavior · Superchallenge problem

A chain on states 1, 2, 3 has these off-diagonal transition probabilities: $P(1 \to 2) = 1/4$, $P(1 \to 3) = 1/2$, $P(2 \to 3) = 1/3$, $P(2 \to 1) = x$, $P(3 \to 1) = 1/6$, $P(3 \to 2) = 1/2$; the remaining probability at each state is for staying put. The chain is reversible, meaning its steady state satisfies $\pi_i P(i \to j) = \pi_j P(j \to i)$ for all $i, j$. What is $\pi_1$? Express your answer as a common fraction.