
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 triangle \( ABC \), let \( E \) be the point where the side \( AC \) is divided into quarters closest to \( C \), and let \( F \) be the midpoint of side \( BC \). The line passing through points \( E \) and \( F \) intersects line \( AB \) at point \( D \). What percentage of the area of triangle \( ABC \) is the area of triangle \( ADE \)?

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