
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 that the area of quadrilateral $ABCD$ is $2021$, and $E$ is a point on $AD$, the centroids of triangles $BCE$, $ABE$, and $CDE$ are $G_1$, $G_2$, and $G_3$ respectively. Determine the area of triangle $G_1 G_2 G_3$.

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