
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
2000 people registered on a new website. Each of them invited 1000 people to be friends. Two people are considered friends if and only if each of them invited the other to be friends. What is the minimum number of friend pairs that could have formed?

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