UMVUE for the centre and half-width of a uniform distribution

Let $X_1,X_2,\dots,X_n$ ($n\ge3$) be a random sample from the uniform distribution on the interval $(\theta_1-\theta_2,\theta_1+\theta_2)$, where $\theta_1\in\mathbb R$ and $\theta_2>0$ are unknown parameters. Let $X_{(j)}$ be the $j^{\text{th}}$ order statistic, $j=1,2,\dots,n$, and let $\bar X=\tfrac1n\sum_{i=1}^nX_i$. Here, $(X_{(1)},X_{(n)})$ is a complete and sufficient statistic for $(\theta_1,\theta_2)$. Then, which of the following statements are true?