
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
Suppose \( x, y, \) and \( z \) are positive numbers satisfying:
\[
\frac{x^2}{y} = 2, \quad \frac{y^2}{z} = 4, \quad \text{and} \quad \frac{z^2}{x} = 8.
\]
Find \( x \).

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