
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 \(\frac{125+\left(\log _{\frac{1}{2}}\left(x^{4}\right)\right)^{3}}{\log _{2}\left(x^{4}\right) \cdot \log _{2}\left(x^{2}\right)+6 \log _{\frac{1}{2}}\left(x^{4}\right)+17 \log _{2}\left(x^{2}\right)-3} \geq 0\).

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