
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
\[ (\log_2 x)^5 + (\log_3 y)^5 + 32 = 16 (\log_2 x)(\log_3 y). \]
Compute \( x^2 + y^2 \).

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