$AL$, $BM$, and $CN$ are the medians of $\triangle ABC$. $K$ is the intersection of the medians. If $C, K, L, M$ are concyclic and $AB = \sqrt{3}$, find the length of the median $CN$. The original answer is in the form \(\frac{k\sqrt{3}}{n}\), where k and n are integers. Please find the value of k + n.

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