
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
Given parallelogram $ABCD$, $AB=4$, $AD=3$, $\overrightarrow{AE}=\frac{1}{3}\overrightarrow{EB}$, $\overrightarrow{DF}=2\overrightarrow{FC}$, and $\overrightarrow{BF}⋅\overrightarrow{CE}=-6$, calculate the area of parallelogram $ABCD$.

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