
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 $a,$ $b,$ and $c$ be nonzero real numbers, and let
\[ x = k\frac{b}{c} + \frac{c}{b}, \quad y = k\frac{a}{c} + \frac{c}{a}, \quad z = k\frac{a}{b} + \frac{b}{a}. \]
where $k$ is a non-zero real constant. Simplify $x^2 + y^2 + z^2 - xyz$.

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