
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 an arm wrestling tournament, there are $2^{n}$ athletes, where $n$ is a natural number greater than 7. For each win, an athlete receives 1 point; for a loss, 0 points. Before each round, pairs are randomly formed from participants who have an equal number of points (those who cannot be paired receive a point automatically). After the seventh round, it turned out that exactly 42 participants had scored 5 points. What is the value of $n$?

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