
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
On the sides \( AC \) and \( BC \) of triangle \( ABC \), points \( D \) and \( E \) are taken respectively. Line segments \( AE \) and \( BD \) intersect at point \( F \). Find the area of triangle \( CDE \) if the areas of triangles \( ABF \), \( ADF \), and \( BEF \) are \( 1 \), \( \frac{1}{3} \), and \( \frac{1}{4} \) respectively.

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