
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
The tower function is defined recursively: $T(1) = 3$ and $T(n + 1) = 3^{T(n)}$ for $n \ge 1$. Let $A = (T(6))^2$ and $B = (T(6))^A$. What is the largest integer $k$ for which \[\underbrace{\log_3\log_3\log_3\ldots\log_3B}_{k\text{ times}}\] is defined?
A) 5
B) 6
C) 7
D) 8

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