
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 tennis tournament, there are 254 schoolchildren participating. For each victory, a participant receives 1 point, and for each loss, they receive 0 points. If the winner initially had fewer points than their opponent, they are additionally awarded one point from the loser. In each round, participants with an equal number of points compete against each other, but one pair can have a difference of 1 point between the participants. The tournament ends as soon as a single leader is determined. How many schoolchildren will finish the tournament with 5 points?

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