
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
Fifteen people sit down for a meal, and there are three choices of meals: beef, chicken, and fish. Five people order beef, five order chicken, and five order fish. The waiter serves the fifteen meals in random order. Find the number of ways in which the waiter could serve the meal types so that exactly three people receive the type of meal they ordered.

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