
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
Let the tower function $T(n)$ be defined as $T(1)=2$ and $T(n+1)=2^{T(n)}$ for $n \ge 1$. Calculate the value of $A = (T(4))^T(4)$, and let $B = (T(4))^A$. Determine the largest integer $k$ such that the value of \[ \underbrace{\log_2\log_2\log_2\ldots\log_2 B}_{k\text{ times}} \] is defined.
- A) 2
- B) 3
- C) 4
- D) 5

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