
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 $z$ be real numbers greater than 1 such that
\[(\log_2 x)^4 + (\log_5 z)^4 + 12 = 12 (\log_2 x)(\log_5 z).\]
Compute $x^{\sqrt{3}} + z^{\sqrt{3}}.$

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