
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 of threes be defined recursively as follows: $S(1) = 3$ and $S(n + 1) = 3^{S(n)}$ for $n\ge1$. Calculate $C = (S(5))^{S(5)}$ and $D = (S(5))^C$. Find the largest integer $m$ for which \[\underbrace{\log_3\log_3\log_3\ldots\log_3D}_{m\text{ times}}\] is defined.
A) 4
B) 5
C) 6
D) 7

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