
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
Solve the inequality: 
\[
\frac{64+\left(\log _{\frac{1}{5}}\left(x^{2}\right)\right)^{3}}{\log _{\frac{1}{5}}\left(x^{6}\right) \cdot \log _{5}\left(x^{2}\right)+5 \log _{5}\left(x^{6}\right)+14 \log _{\frac{1}{5}}\left(x^{2}\right)+2} \leq 0.
\]

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