
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
There are  $1000$  students in a school. Every student has exactly  $4$  friends. A group of three students  $ \left \{A,B,C \right \}$  is said to be a *friendly triplet* if any two students in the group are friends. Determine the maximal possible number of friendly triplets.

*Proposed by Nikola Velov*

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