
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 soccer league with \( n \) teams ( \( n > 3 \) ) held \( k \) matches. Each pair of teams played at most one match, and there were no draws. It was found that exactly one team remained unbeaten. Furthermore, for any two teams \( A \) and \( B \), there exists another team \( C \) such that either \( A \) defeated \( C \) and \( B \) defeated \( C \), or \( C \) defeated \( A \) and \( C \) defeated \( B \). Determine the minimum possible value of \( k \).

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