
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 $T(n)$ recursively by: $T(1) = 3$ and for $n \geq 1, T(n+1) = 3^{T(n)}$. Let $A = T(6)^{T(6)}$ and $B = T(6)^A$. How many times can you apply $\log_3$ to $B$ before the result is no longer defined?

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