
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 and B each have 7 players who will compete in a Go tournament in a predetermined order. The first player from each team plays against each other. The loser is eliminated, and the winner plays against the second player from the losing team, and so on. This continues until all players from one team are eliminated and the other team wins. What is the probability that Team A eliminates 6 players before winning?

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