
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
3n (≥ 5) teams participate in a round-robin tournament. The winner of a match gets 3 points, both teams get 1 point each for a tie, and the loser gets 0 points. The team ranked third from last has fewer points than those ranked above it but more points than the last two teams. Additionally, this team's number of wins is more than those ranked above it but fewer than the last two teams. What is the minimum value of n?

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