
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
Given the function \( f(x) = \left(\frac{1}{a^{x}-1} + \frac{1}{2}\right) x^{2} + b x + 6 \) (where \(a\) and \(b\) are constants and \(a > 1\)), and \( f(\log \log_{8} 1000) = 8 \), find the value of \( f(\log \log 2) \).

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