
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 $M$ be the midpoint of the segment joining vertices $A$ and $B$ of triangle $ABC$, and let $Q$ be an arbitrary point. Then there exists a constant $k$ so that
\[ QA^2 + QB^2 + QC^2 = k \cdot QM^2 + MA^2 + MB^2 + MC^2. \]
Find $k$.

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