
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
In a school gym, there is one arm-wrestling table. The physical education teacher organized a school tournament. He calls any two participants who have not yet faced each other to a match. There are no ties. If a participant suffers a second defeat, they are eliminated from the tournament. After 29 matches, all participants have been eliminated except for two. How many students participated in the tournament?

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