
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
In a group of 9 people, arrange for each person to shake hands with exactly 2 other people in the group. Two handshake arrangements are considered different if and only if there exists at least one pair of people who shake hands in one arrangement but not in the other. How many different handshake arrangements are possible? (2012 AIME Problem)

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