
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
Let \( u, v, w \) be positive real numbers, all different from 1. If
\[
\log_{u}(vw) + \log_{v}(w) = 5 \quad \text{and} \quad \log_{v}(u) + \log_{w}(v) = 3,
\]
find the value of \( \log_{w}(u) \).

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