
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
For all non-zero numbers $x$ and $z$ such that $x = \frac{1}{z^2}$, compute the value of $\left(x - \frac{1}{x}\right)\left(z^2 + \frac{1}{z^2}\right)$.
A) $2x^2$  
B) $2z^4$  
C) $x^2 + z^4$  
D) $x^2 - z^4$  
E) $x^4 - z^2$

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