Show how to synthesize $2-$methylhexanoic acid using either the malonic ester synthesis or the acetoacetic ester synthesis and reagent$($s$)$ from the table provided below.

Indicate which synthesis is used by choosing between Malonic Ester or Acetoacetic Ester as the starting material.

The starting material for this synthesis is:

From the choices provided, list the reagent$($s$)$ in order that will accomplish this transformation. No more than $6$ steps are required.

List your answer as a single letter $($single$-$step transformation$)$ or a series of letters $($multi$-$step transformation$)$ with no commas separating them.

For example, $"$ai$"$ corresponds to:

$1.$ EtO$-$Na$+$

$2.$ CH$3$CH$2$Br