
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 $H$ be the orthocenter of triangle $ABC.$ For all points $Q$ on the circumcircle of triangle $ABC,$ 
\[QA^2 + QB^2 + QC^2 - QH^2\] is a constant. Express this constant in terms of the side lengths $a', b', c'$ (where $a' = ka$, $b' = kb$, $c' = kc$ for some constant $k$) and circumradius $R'$ of triangle $ABC$.

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