
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
A number of couples met and each person shook hands with everyone else present, but not with themselves or their partners. There were 31,000 handshakes altogether. How many couples were there?

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