
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
Twelve people sit down for dinner where there are four choices of meals. Three people each order beef, chicken, fish, and vegetarian meals. The waiter serves the twelve meals in random order. Find the number of ways the waiter could serve the meal types such that exactly two persons receive the type of meal they ordered.

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