In an equilateral triangle \( \triangle ABC \) with side length \( s \), a point \( D \) is on side \( BC \) such that \( BD:DC = 2:1 \). Let \( E \) be the midpoint of \( AD \). Determine the ratio of the area of \( \triangle ABE \) to the area of \( \triangle ABC \). Let's think step by step and output the final answer within \boxed{}.
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