
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
\[
(\log_{2} x)^{4} - \left(\log_{\frac{1}{2}} \frac{x^3}{8}\right)^{2} + 9 \cdot \log_{2} \frac{32}{x^{2}} < 4 \cdot (\log_{\frac{1}{2}} x)^{2}
\]

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