
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 \[(\log_2 x)^3 + (\log_3 y)^3 + 6 = 6 (\log_2 x)(\log_3 y).\] Compute $x^{\sqrt{3}} + y^{\sqrt{3}}.$

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