Size and power of a given critical region

Let $X_1$ and $X_2$ be a random sample of size $2$ from a discrete distribution with the probability mass function

$$f(x;\theta)=P(X=x)=\begin{cases}\theta, & x=0,\ 1-\theta, & x=1,\end{cases}$$

where $\theta\in\Theta=\{0.2,0.4\}$ is the unknown parameter. For testing $H_0:\theta=0.2$ against $H_1:\theta=0.4$, consider a test with the critical region

$$C=\{(x_1,x_2)\in\{0,1\}\times\{0,1\}:x_1+x_2<2\}.$$

Let $\alpha$ and $\beta$ denote the probability of Type I error and power of the test, respectively. Then $(\alpha,\beta)$ is