
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
Given $5$ A's, $5$ B's, and $5$ C's, calculate the number of $15$-letter arrangements with no A's in the first $5$ letters, no B's in the next $5$ letters, and no C's in the last $5$ letters.

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