
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:
\[(\log_4 x)^3 + (\log_5 y)^3 + 9 = 12 (\log_4 x)(\log_5 y).\]
Compute $x^2 + y^2.$

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