
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 round robin tournament is held with  $2016$  participants. Each player plays each other player once and no games result in ties. We say a pair of players  $A$  and  $B$  is a *dominant pair* if all other players either defeat  $A$  and  $B$  or are defeated by both  $A$  and  $B$ . Find the maximum number dominant pairs.

[i]Proposed by Nathan Ramesh

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