A $23$ $kg$ cabinet is mounted on castors allowing it to move freely on the floor. If a $204$ $N$ force ($F$) is applied, determine the acceleration of the centre of gravity, and the range of $h$ in $mm$ for which the cabinet will not tip.

$d = 625$ $mm$

$b = 380$ $mm$

$a_{G}$ = $m/s^2$

$h_{max}$ = $mm$

$h_{min}$ = $mm$