
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, \(2^n + 4\) schoolchildren are participating, where \(n\) is a natural number greater than 4. Each win awards 1 point, and each loss awards 0 points. Before each round, pairs are formed by drawing lots from participants with the same number of points (those who cannot find pairs skip the round). The tournament ends when a sole leader is determined. How many schoolchildren will have scored exactly 3 points by the end of the tournament?

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