Complete the following reaction sequence.
$CH_3-CO-CH_3$ $\xrightarrow[(ii) H_2O]{(i) CH_3MgBr} [A]$ $\xrightarrow{Na, \text{Ether}} [B]$ $\xrightarrow{CH_3-Br} [C]$

(N/A) Step $1$: Reaction of propanone with $CH_3MgBr$ followed by hydrolysis gives $2$-methylpropan-$2$-ol $([A])$.
$CH_3-CO-CH_3 + CH_3MgBr$ $\rightarrow (CH_3)_3C-OMgBr$ $\xrightarrow{H_2O} (CH_3)_3C-OH$ $([A])$.
Step $2$: Reaction of $[A]$ with $Na$ metal in ether gives sodium $tert$-butoxide $([B])$.
$(CH_3)_3C-OH + Na \rightarrow (CH_3)_3C-ONa$ $([B])$ $+ \frac{1}{2} H_2$.
Step $3$: Reaction of $[B]$ with $CH_3-Br$ via Williamson synthesis gives $2$-methoxy-$2$-methylpropane $([C])$.
$(CH_3)_3C-ONa + CH_3-Br \rightarrow (CH_3)_3C-O-CH_3$ $([C])$ $+ NaBr$.