
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
Define the tower function $T'(n)$ as follows: $T'(1) = 3$ and for $n \ge 1$, $T'(n + 1) = 3^{T'(n)}$. Let $A' = (T'(4))^{T'(4)}$ and $B' = (T'(4))^{A'}$. Determine the largest integer $k$ for which:
\[
\underbrace{\log_3\log_3\ldots\log_3 B'}_{k\text{ times}}
\]
is defined.
A) 4
B) 5
C) 6
D) 7
E) 8

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