
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 \(a,\) \(b,\) \(c,\) and \(d\) be nonzero real numbers, and let:
\[
x = \frac{b+d}{c+d} + \frac{c+d}{b+d}, \quad y = \frac{a+d}{c+d} + \frac{c+d}{a+d}, \quad z = \frac{a+d}{b+d} + \frac{b+d}{a+d}.
\]
Simplify \(x^2 + y^2 + z^2 - xyz.\)

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