
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 9 and point \(P\) is located inside the quadrilateral. Let the centroids of triangles \(\triangle ABP\), \(\triangle BCP\), \(\triangle CDP\), and \(\triangle DAP\) be \(G_1\), \(G_2\), \(G_3\), and \(G_4\) respectively. Find the area of quadrilateral \(G_1G_2G_3G_4\).

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