
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
The sports event lasted for \( n \) days; \( N \) sets of medals were awarded; on the 1st day, 1 set of medals and \( \frac{1}{7} \) of the remaining sets were awarded; on the 2nd day, 2 sets of medals and \( \frac{1}{7} \) of the remaining sets were awarded; on the next to last, \( (n-1) \)th day, \( (n-1) \) sets of medals and \( \frac{1}{7} \) of all remaining sets were awarded; finally, on the last day, the remaining \( n \) sets of medals were awarded. How many days did the sports event last and how many sets of medals were awarded?

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