
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 isosceles triangle with $AB = AC = 3$ cm and $BC = 4$ cm. Extend $\overline{BC}$ to $D$ such that $\overline{CD} = BC$. Let $E$ be the midpoint of $\overline{AB}$, and suppose a circle with radius having center at $E$ and passing through $B$ intersects $\overline{AC}$ at point $F$ above $C$. Find the area of quadrilateral $BEFC$ in square centimeters.

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