JEE 2016! (will vectors help?)

The Pentagon $ABCDE$ has the properties $AB || CD , ED || BC , \dfrac{AB}{CD} = \dfrac12 , \dfrac{ED}{BC} = \dfrac13$ .

Given that the straight lines $AD$ and $CE$ intersect at point $O$ to form the ratios $\dfrac{OC}{EO} = \dfrac ab$ and $\dfrac{OD}{AO} = \dfrac cd$ , where $a,b,c,d$ are positive integers with $\gcd(a,b) = \gcd(c,d) = 1$ .

Find the value of $a+b+c+d$ .