
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 a meal where there are four choices: beef, chicken, fish, and vegetarian. Each meal type is ordered by three people. The waiter serves the twelve meals in random order. Determine the number of ways in which the waiter could serve the meal types so that exactly two people receive the type of meal they ordered.

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