
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
If $xy = p$, $xz = q$ and $yz = r$ with $x, y, z \neq 0$, find the expression for $x^3+y^3+z^3$ in terms of $p$, $q$, and $r$.
A) $\frac{p^2 q^2 + p^2 r^2 + q^2 r^2}{pqr}$
B) $\frac{p^2 + q^2 + r^2}{pqr}$
C) $\frac{p + q + r}{pqr}$
D) $\frac{(pq + pr + qr)^2}{pqr}$
E) $\frac{(pq)^2 + (pr)^2 + (qr)^2}{pqr}$

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