
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
The organizers of a ping-pong tournament have only one table. They call two participants to play, who have not yet played against each other. If after the game the losing participant suffers their second defeat, they are eliminated from the tournament (since there are no ties in tennis). After 29 games, it turned out that all participants were eliminated except for two. How many participants were there in the tournament?

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