
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 $BC = 2$ cm. Extend $\overline{AB}$ to $D$ so that $BD = BC$. Let $F$ be the midpoint of $\overline{AC}$. Suppose $\overline{DF}$ meets $\overline{BC}$ at point $E$. Find the area of the quadrilateral $AFEC$ in square centimeters.

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