
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 length $\frac{p}{q}$ of the domain of the function \( f(x) = \log_4\left(\log_{16}\left(\log_4\left(\log_{\frac{1}{16}}\left(\left(\log_{16} x\right)^2\right)\right)\right)\right) \), where \( p \) and \( q \) are relatively prime positive integers. What is \( p+q \)?
**A)** 90
**B)** 100
**C)** 230
**D)** 241
**E)** 260

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