Uncertainty and Pareto efficient policies

There are two economic agents $iin {1,2}$ with state dependent utility $u_{is}=-(x-b_{is})^2$ where $xin R$ and $b_{is}in R$ is bliss point of $i$ in state $sin{1,2}$. Assume $b_{1s}lt b_{2s}$ for $forall sin{1,2}$. State $sin{1,2}$ occurs with probability $pi_{s}$. We denote $U_i(x_1,x_2)=pi_1u_{i1}(x_1)+pi_2u_{i2}(x_2)$.

Ex-post Pareto efficient policies in state 1 and 2, $x_1^*$ and $x_2^*$ respectively, I found them to be as follows:

Any policy in $[b_{11},b_{21}]$ is ex- post Pareto efficient in state 1 and any policy not in $[b_{11},b_{21}]$ is ex-post Pareto inefficient in state 1. Hence $x_1^* = z$, where $z$ is any $zin [b_{11}, b_{21}].$ By similar arguments $x_2^* = z$, where $z$ is any $zin[b_{12}, b_{22}].$

But how would we characterize ex-ante Pareto efficient policy pairs, ${x_1^*,x_2^*}?$