
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
Three teams, A, B, and C, participate in a go tournament, each consisting of 9 players. The rules are as follows: Each match involves one player from two different teams, with the winner continuing to compete, and the loser being eliminated. Another player from the third team then competes against the winner. The tournament starts with a match between A and B. The process continues in this manner. If all 9 players from one team are eliminated, the remaining two teams continue competing until one team is entirely eliminated. The team of the winner of the final match is the champion team. Please answer:
(1) What is the minimum number of matches the champion team must win?
(2) If the champion team wins 11 matches, how many matches at least were played in total?

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