
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 chess tournament, each participant played exactly one match against each other participant. Winners earned 1 point, losers earned 0 points, and each earned 1/2 point if there was a tie. After the tournament concluded, it was noted that exactly half of the points each player earned were from the fifteen players with the lowest scores. Specifically, each of these fifteen lowest scoring players obtained half of their points from matches with the other fourteen of these fifteen. Determine the total number of players in the tournament.

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