For $f(x)=\sin x+3x-\dfrac{2}{\pi}(x^{2}+x)$, where $x\in\left[0,\tfrac{\pi}{2}\right]$, consider: (I) $f$ is increasing in $\left(0,\tfrac{\pi}{2}\right)$. (II) $f'$ is decreasing in $\left(0,\tfrac{\pi}{2}\right)$.