
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 \( x \) and \( y \) be real numbers greater than 1 such that
\[(\log_2 x)^3 + (\log_3 y)^3 + 9 = 9 (\log_2 x)(\log_3 y).\]
Compute \( x^{\sqrt{3}} + y^{\sqrt{3}}. \)

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