
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 15-letter arrangements of 5 A's, 5 B's, and 5 C's have no C's in the first 5 letters, no B's in the next 5 letters, and no A's in the last 5 letters?
A) $\sum_{k=0}^{5}\binom{5}{k}^{2}$
B) $\sum_{k=0}^{5}\binom{5}{k}^{3}$
C) $3^5 \cdot 2^5$
D) $\frac{15!}{(5!)^3}$
E) $3^{15}$

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