
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 $p$, $q$, $r$, and $s$ be the roots of $x^4 - 24x^3 + 50x^2 - 26x + 7 = 0$. Compute \[(p+q)^2 + (q+r)^2 + (r+s)^2 + (s+p)^2 + (p+r)^2 + (q+s)^2.\]

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