
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 that \(x\), \(y\), and \(z\) satisfy the following system of equations:

\[
\begin{cases}
\log_{2}\left(x y z - 3 + \log_{5} x \right) = 5, \\
\log_{3}\left(x y z - 3 + \log_{5} y \right) = 4, \\
\log_{4}\left(x y z - 3 + \log_{5} z \right) = 4,
\end{cases}
\]

find the value of \(\log_{5} (x y z)\).

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