Let $[x]$ denote the greatest integer $\leq x$, where $x \in \mathbf{R}$. If the domain of the real valued function
$\mathrm{f}(\mathrm{x})=\sqrt{\frac{[\mathrm{x}] \mid-2}{[\mathrm{x}] \mid-3}}$ is $(-\infty, a) \cup[b, c) \cup[4, \infty)$,a < b < c, then the value of a+b+c is:
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