
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 \( u \) and \( v \) be real numbers greater than 1 such that
\[
(\log_3 u)^3 + (\log_5 v)^3 + 6 = 6 (\log_3 u)(\log_5 v).
\]
Compute \( u^{\sqrt{3}} + v^{\sqrt{3}} \).

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