A trapezoid $ABCD$ lies on the $xy$-plane. The slopes of lines $BC$ and $AD$ are both $\frac 13$, and the slope of line $AB$ is $-\frac 23$. Given that $AB=CD$ and $BC< AD$, the absolute value of the slope of line $CD$ can be expressed as $\frac mn$, where $m,n$ are two relatively prime positive integers. Find $100m+n$.

[i] Proposed by Yannick Yao [/i]