
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
Given \( x, y \in \mathbf{R}_{+}, x \neq 1, y \neq 1 \), such that \(\log _{2} x = \log _{y} 16\) and \( x y = 64 \), find the value of \(\left(\log _{2} \frac{x}{y}\right)^{2} \).

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