Let $[ABCD]$ be a convex quadrilateral with an area of $2014$, and let $P$ be a point on $[AB]$ and $Q$ a point on $[AD]$ such that triangles $[ABQ]$ and $[ADP]$ have an area of $1$. Let $R$ be the intersection of $[AC]$ and $[PQ]$. Determine $\frac{\overline{RC}}{\overline{RA}}$.

Let's think step by step and output the final answer within \boxed{}.
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