
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
Triangle \(ABC\) has side lengths \(AB=2\sqrt{5}\), \(BC=1\), and \(CA=5\). Point \(D\) is on side \(AC\) such that \(CD=1\), and \(F\) is a point such that \(BF=2\) and \(CF=3\). Let \(E\) be the intersection of lines \(AB\) and \(DF\). Find the area of \(CDEB\).

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