
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 a point inside triangle $ABC$ such that $G' = \frac{1}{4}A + \frac{1}{4}B + \frac{1}{2}C$. Let $Q$ be another arbitrary point. Determine the constant $k'$ such that
\[ QA^2 + QB^2 + QC^2 = k' \cdot QG'^2 + GA^2 + GB^2 + GC^2. \]

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