
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 $a, b, c, d$ be nonzero real numbers, and define
\[
x = \frac{b}{c} + \frac{c}{b}, \quad y = \frac{a}{c} + \frac{c}{a}, \quad z = \frac{a}{b} + \frac{b}{a}, \quad w = \frac{a}{d} + \frac{d}{a}
\]
Simplify the expression $x^2 + y^2 + z^2 + w^2 - xyzw$.

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