What is the maximum area of a triangle that can be inscribed in an ellipse with semi-axes $a$ and $b$? Express your answer in terms of $a$ and $b$. The original answer is in the form $ab\frac{k\sqrt{3}}{m}$, where $k$ and $m$ are integers. Please give the value of $k + m$.

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