
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 \( x^2 \) and \( y \) vary inversely where \( x \) and \( y \) are both positive integers. Given that \( y = 16 \) when \( x = 4 \), and additionally, \( z \) (where \( z = x - y \)) is given to be 10 when \( y = 4 \), find the value of \( x \) when \( y = 256 \).

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