One Sweep Then Greedy

A two-state MDP, $\gamma = 0.9$, all transitions deterministic.

state	action	reward	next state
$s_1$	$a$	1	$s_1$
$s_1$	$c$	0	$s_2$
$s_2$	$b$	0	$s_1$
$s_2$	$d$	2	$s_2$

The current policy $\pi$ takes $a$ in $s_1$ and $b$ in $s_2$. Policy evaluation is run to convergence, then one policy improvement step is taken.

Which action does the improved policy take in $s_2$?