
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
Let $ABC$ be an equilateral triangle where each side is 3 cm long. Extend $\overline{AB}$ to point $D$ such that $AB = BD$. Let $E$ be the midpoint of $\overline{BC}$. Line $\overline{ED}$ intersects $\overline{AC}$ at point $F$. Calculate the area of quadrilateral $BEFC$.

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