Let $ABCD$ be a trapezoid such that $AB \parallel CD$, $|AB|<|CD|$, and $\text{Area}(\triangle ABC)=30$. Let the line through $B$ parallel to $AD$ meet $[AC]$ at $E$. If $|AE|:|EC|=3:2$, then what is the area of trapezoid $ABCD$?

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