
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

Given a trapezoid \(ABCD\). A line parallel to the bases intersects the legs \(AB\) and \(CD\) at points \(M\) and \(N\) respectively. A point \(E\) is taken on the base \(BC\). The segments \(AE\) and \(ED\) intersect \(MN\) at points \(S\) and \(T\). The areas of triangles \(AMS\), \(SET\), and \(TND\) are 12, 8, and 15, respectively. What is the minimum possible area of the trapezoid given these conditions?

Present the answer in LaTex format: \boxed{Your answer}
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