
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 $ABCDE$ be a convex pentagon, and let $G_A,$ $G_B,$ $G_C,$ $G_D,$ $G_E$ denote the centroids of triangles $BCDE,$ $ACDE,$ $ABDE,$ $ABCE,$ and $ABCD,$ respectively. Find $\frac{[G_A G_B G_C G_D G_E]}{[ABCDE]}.$

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