
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
First, three people, and then four people shook hands with each other. How many handshakes were there? Find the pattern in counting the number of handshakes and determine the number for 7 people.

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