
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 a right triangle with $∠ACB = 90°$, side $\overline{AB} = 3$ cm, and side $\overline{BC} = 4$ cm. $\overline{AB}$ is extended to point $D$ such that $D$ is twice the distance from $A$ to $B$. Point $E$ is the midpoint of $\overline{CB}$. Line $\overline{ED}$ intersects $\overline{AC}$ at point $F$. Compute the area of quadrilateral $AEFC$ in square centimeters.

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