
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
\[8.31 \frac{4 x^{2}-1}{\log _{1,7}\left(\frac{1}{2}\left(1-\log _{7} 3\right)\right)} \leq 0\]

\[8.320,5^{x-2}>6\]

\[8.330,3^{\log _{1} \log _{2} \frac{3 x+6}{x^{2}+2}}>1\]

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