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

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