The coefficient of the term independent of $x$ in the expansion of $(1+x+2x^3)\bigg(\large\frac{3}{2}$$x^2-\large\frac{1}{3x}$$\bigg)^9$ is

Question

$\begin{array}{1 1} \frac{1}{3} \\ \frac{19}{54} \\ \frac{17}{54} \\ \frac{1}{4} \end{array}$