
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 real numbers greater than 1 such that
\[ 
\begin{aligned}
x^{\log _{y} z} & = 2, \\
y^{\log _{y} x} & = 4, \\
z^{\log _{x} y} & = 8 .
\end{aligned}
\]
Compute \(\log _{x} y\).

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