
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 $p, q, r$ be nonzero real numbers, and define:
\[x = \frac{q}{r} + \frac{r}{q}, \quad y = \frac{p}{r} + \frac{r}{p}, \quad z = \frac{p}{q} + \frac{q}{p}.\]
Find and simplify $x^2 + y^2 + z^2 - 2xyz.$

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