
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
Consider the function \( g(x) = \log_{4}(\log_{\frac{1}{4}}(\log_{8}(\log_{\frac{1}{8}}x))) \). Determine the length of the domain of \( g(x) \) as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are relatively prime positive integers. What is \( p+q \)?
A) 18868667
B) 20971518
C) 1771561
D) 8388608
E) 16777216

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