
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 such that \(u > 16\) and \(v > 27\). Find the value of \(u^3 + v^3\) given that:
\[
(\log_4 u)^5 + (\log_3 v)^5 + 36 = 12 (\log_4 u)(\log_3 v).
\]

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