
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
If a parabola passes through the origin, point $A(6,6)$, and point $B(-6,6)$, and point $C$ is a point on the $x$-axis, such that the centroid $G$ of triangle $ABC$ lies on the parabola, then the coordinates of point $G$ are ______.

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