
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
 $2017$  chess players participated in the chess tournament, each of them played exactly one chess game with each other. Let's call a trio of chess players  $A, B, C$  a *principled*one, if  $A$  defeated  $B$ ,  $B$  defeated  $C$ , and  $C$  defeated  $A$ . What is the largest possible number of threes of principled chess players?

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