
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
Let \( \square ABCD \) be a trapezoid with parallel sides \( AB \) and \( CD \) of lengths 6 units and 8 units, respectively. Let \( E \) be the point of intersection of the extensions of the nonparallel sides of the trapezoid. If the area of \( \triangle BEA \) is 60 square units, what is the area of \( \triangle BAD \) ?

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