Find the value of the following expression: $\frac{1\frac{1}{2}+1\frac{3}{7}÷(1\frac{3}{5}\, of\, 1\frac{1}{4})×2\frac{1}{3}}{2\frac{2}{3}÷\frac{4}{9}×\frac{5}{6}+14}$

$\frac{107}{342}$ $\frac{49}{114}$ $\frac{13}{114}$ $\frac{1}{6}$

$\frac{1}{6}$