
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
What are all real numbers \( x > 0 \) for which \( \log_{2}(x^{2}) + 2 \log_{x} 8 = \frac{392}{\log_{2}(x^{3}) + 20 \log_{x}(32)} \)?

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