
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
Let \(P\) be a point coincident with vertex \(A\) of triangle \(ABC\). Let \(G_1\), \(G_2\), and \(G_3\) be the centroids of triangles \(PBC\), \(PCA\), and \(PAB\) respectively. If the area of triangle \(ABC\) is 24, find the area of triangle \(G_1 G_2 G_3\).

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