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Let $\triangle LMN$ be a triangle with an area of $1$ square unit and $X$ is the midpoint of side $MN$. $P$ and $Q$ are two points on sides $LM$ and $LN$ respectively such that $LP=2PM$ and $NQ=2LQ$. Lines $LX$ and $PQ$ intersect each other at point $Y$. The area of $\triangle LYQ$ can be expressed as $\frac {a}{b}$, where $a, b$ are co-prime. Determine $a+b$.


Geometry  


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