
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 the square \(ABCD\), \(E\) and \(F\) are trisection points of the diagonal \(BD\). The line extending \(AE\) intersects \(BC\) at \(G\), and the line extending \(GF\) intersects \(AD\) at \(H\). Given that the area of \(\triangle DHF\) is 12, find the area of the square \(ABCD\).

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