Let $ABCDEF$ be a convex hexagon. $AD$ intersects $BE$ at $G$, $BE$ intersects $CF$ at $H$, and $AD$ intersects $CF$ at $I$. Additionally, $GF$ intersects $IE$ at $J$, $HD$ intersects $GC$ at $K$, and $IB$ intersects $HA$ at $L$. Let $[\mathcal{P}]$ denote the area of polygon $\mathcal{P}$. Given that \begin{align*} [GHI] &= 4 \\ [GDE] &= 5 \\ [HBC] &= 6 \\ [IFA] &= 7 \end{align*} find the minimum possible value of $[JFE] + [KDC] + [LBA] – [GKHLIJ]$.