
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 parallelogram $ABCD$, point $E$ is on the side $AB$, and the ratio $AE:EB = 1:2$. $DE$ intersects $AC$ at point $F$. If the area of triangle $AEF$ is $6\, \text{cm}^2$, then the area of triangle $ABC$ is $\boxed{18\, \text{cm}^2}$.

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