The null density is uniform

Let X be a random variable with the probability density function $f(x)=2\theta x+2(1-\theta )(1-x)$ if 0 < x < 1, and 0 otherwise, where $\theta \in [0,1]$. Based on single observation x, the critical region of the most powerful test for testing null hypothesis $H_0:\theta =1/2$ against alternative hypothesis $H_1:\theta =1$, at level of significance $\alpha =0.25$, is