
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 $G$ be the centroid of triangle $ABC$, and define $s_1=GA+GB+GC$ where $GA$, $GB$, and $GC$ are the distances from $G$ to the triangle's vertices. Let $s_2=AB+BC+CA$ still represent the perimeter. Determine the relationship between $s_1$ and $\frac{1}{3}s_2$.
A) $s_1 = \frac{1}{3} s_2$
B) $s_1 < \frac{1}{3} s_2$
C) $s_1 > \frac{1}{3} s_2$
D) $s_1 = \frac{1}{2} s_2$
E) None of these

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