
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 real numbers $x$ and $z$ such that $x = \sqrt{z}$, evaluate the expression $\left(x - \frac{1}{x}\right)\left(\sqrt{z} + \frac{1}{\sqrt{z}}\right)$.
A) $z$
B) $\frac{1}{z}$
C) $z + \frac{1}{z}$
D) $z - \frac{1}{z}$

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