
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
If $x \neq 0, x^2 = 8y$ and $x^2 = 128y^2$, find the value of $x$.
A) \( \sqrt{2} \)
B) \( \frac{1}{2} \)
C) \( \frac{\sqrt{2}}{2} \)
D) \( \frac{1}{\sqrt{2}} \)

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