Gambler's Ruin with Alternating Bias

A gambler moves on $\{0, 1, 2, 3, 4, 5, 6\}$ with absorbing barriers at $0$ and $6$. The win probability depends on the current position: at odd states ($k = 1, 3, 5$), $p = 0.6$; at even states ($k = 2, 4$), $p = 0.4$. (Win means $+1$, loss means $-1$.) Starting from state $3$, find the probability of reaching $6$ before $0$, and the expected number of steps until absorption.