
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 3cm. $\overline{BC}$ is extended to $D$ such that $CD = BC$, and $E$ is the midpoint of $\overline{AC}$. Suppose $\overline{ED}$ meets $\overline{AB}$ at $F$. Find the area of the quadrilateral $BEFC$ in square centimeters.

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