
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
Given $x + y = p$, $y + z = q$, and $z + x = r$, none of which are zero, find the value of $x^2 + y^2 + z^2$.
A) $\frac{p^2 + q^2 + r^2}{2}$
B) $\frac{p^2 + q^2 + r^2 - pq - qr - rp}{2}$
C) $\frac{(p+q+r)^2}{2}$
D) $\frac{p^2 + q^2 + r^2 + pq + qr + rp}{2}$
E) $\frac{(p+q+r)^2 - pq - qr - rp}{2}$

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