
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
Let \( g(x) = \log_{\frac{1}{3}}\left(\log_9\left(\log_{\frac{1}{9}}\left(\log_{81}\left(\log_{\frac{1}{81}}x\right)\right)\right)\right) \). Determine the length of the interval that forms the domain of \( g(x) \), and express it in the form \( \frac{p}{q} \), where \( p \) and \( q \) are relatively prime positive integers. What is \( p+q \)?
A) 80
B) 82
C) 84
D) 86
E) 88

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