
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
Find the minimum value of
\[\frac{x^3}{y - 1} + \frac{y^3}{x - 1}\]
for real numbers $x > 1$, $y > 1$ with the additional condition $xy = 4$.

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