
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 an equilateral triangle $ABC$, and let $Q$ be a point such that vector $\vec{QA}$ is the same as vector $\vec{BC}$. Then there exists a constant $k'$ such that:
\[
QA^2 + QB^2 + QC^2 = k' \cdot QG^2 + GA^2 + GB^2 + GC^2.
\]
Find $k'$.

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