
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
Teams A, B, and C are competing in a Go tournament, each with 9 players. The rules are as follows: In each match, one player from each of two teams competes. The winner stays on, and the loser is eliminated; the other team then sends in a new challenger. The matches continue in this manner, starting with teams A and B each sending one player. When a team loses all 9 players, the remaining two teams continue the tournament until another team is completely eliminated. The team of the final match's winner is the champion team.
Answer the following questions and explain your reasons:
(1) What is the minimum number of matches the champion team must win?
(2) If by the end of the tournament, the champion team has won 11 matches, what is the minimum number of matches that must have been played in total?

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