
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
Points \(D\) and \(E\) are taken on the sides \(AC\) and \(BC\) of triangle \(ABC\), respectively. The segments \(AE\) and \(BD\) intersect at point \(F\). Find the area of triangle \(CDE\) if the areas of triangles \(ABF\), \(ADF\), and \(BEF\) are equal to \(1\), \(\frac{1}{2}\), and \(\frac{1}{4}\), respectively.

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