
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
In a square \( ABCD \), points \( E \) and \( F \) are the midpoint of side \( AB \) and the trisection point of side \( BC \), respectively. It is known that the area of triangle \( ADE \) is 27 greater than the area of triangle \( CDF \). Determine the area of the square \( ABCD \).

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