
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
\(ABC\) is an equilateral triangle with sides equal to 4 cm. \(BC\) is extended by double its own length to \(D\), and \(E\) is the midpoint of \(AB\). Suppose line \(ED\) intersects line \(AC\) at \(F\). Find the area of the quadrilateral \(BEFC\).

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