
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
Find the domain length $\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, for the function:
\[ f(x) = \log_{\frac{1}{3}}\left(\log_8\left(\log_{\frac{1}{8}}\left(\log_{8}\left(\log_{\frac{1}{8}}x\right)\right)\right)\right). \]
A) 20188567
B) 20988567
C) 21988567
D) 20998667

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