p-value for a Beta shape test

Let $X_{1},X_{2}$ be a random sample of size $2$ from a distribution with the probability density function $$f(x)=\begin{cases}\alpha x^{\alpha-1},&0<x<1,\\0,&\text{otherwise,}\end{cases}$$ where $\alpha>0$ is an unknown parameter. To test $H_{0}:\alpha=1$ against $H_{1}:\alpha=2$, the most powerful test is being used. If the observed value of the random sample is $\dfrac{1}{4},\dfrac{1}{2}$, then the $p$-value of the test equals __________ (rounded off to three decimal places)