
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
In a competition, there were  $2n+1$  teams. Every team plays exatly once against every other team. Every match finishes with the victory of one of the teams. We call cyclical a 3-subset of team  ${ A,B,C  }$   if  $A$  won against  $B$ ,  $B$  won against  $C$  ,  $C$  won against  $A$ .

(a) Find the minimum of cyclical 3-subset (depending on  $n$ );
(b) Find the maximum of cyclical 3-subset (depending on  $n$ ).

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