
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
The set \( M = \{1, 2, \cdots, 12\} \) composed of the first 12 positive integers needs to be divided into four subsets \( M_{1}, M_{2}, M_{3}, M_{4} \) each containing three elements, such that in each subset, one number is the sum of the other two numbers. Find the number of different ways to achieve this division.

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