
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
How many $18$-letter arrangements of $6$ A's, $6$ B's, and $6$ C's have no A's in the first $6$ letters, no B's in the next $6$ letters, and no C's in the last $6$ letters?
A) $\sum_{k=0}^{6} \binom{6}{k}^{3}$
B) $4^{6} \cdot 3^{6}$
C) $3^{18}$
D) $\frac{18!}{(6!)^{3}}$

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