
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
Point \\(P\\) moves on the hyperbola with foci \\(F_1\\) and \\(F_2\\), given by the equation \\( \dfrac{x^2}{16} - \dfrac{y^2}{9} = 1 \). Find the equation of the trajectory of the centroid \\(G\\) of triangle \\(\Delta F_1F_2P\\).

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