Let $f : R \to R$ be a twice differentiable function such that $f''(x) > 0$ for all $x \in R$ and $f'(a-1) = 0$, where $a$ is real number. Let

$g(x) = f(\tan x - 2\tan x + a), \quad 0 < x < \frac{\pi}{2}$

Consider the following two statements:

(I) $g$ is increasing in $\left(0, \frac{\pi}{4}\right)$

(II) $g$ is decreasing in $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$

Then,