A point \(P\) is chosen at random in the interior of equilateral triangle \(ABC\). What is the probability that \(\triangle ABP\) has a greater area than each of \(\triangle ACP\) and \(\triangle BCP\)? Express your answer in the form \(\frac{k}{m}\), where \(k\) and \(m\) are coprime positive integers. Find the value of \(k + m\).

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