
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
In the diagram, $ABCD$ is a parallelogram, $F$ is on $AD$, the area of $\triangle AEF$ is $8 \text{ cm}^2$, the area of $\triangle DEF$ is $12 \text{ cm}^2$, the area of quadrilateral $BCDF$ is $72 \text{ cm}^2$. Find the area of $\triangle CDE$.

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