
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
An athletic meet lasted for \( n \) consecutive days and awarded a total of \( m \) medals. On the first day, 1 medal was awarded plus \(\frac{1}{7}\) of the remaining \( m-1 \) medals. On the second day, 2 medals were awarded plus \(\frac{1}{7}\) of the remaining medals. On each subsequent day, this pattern continued. On the final, \( n \)-th day, exactly \( n \) medals were awarded. Find the values of \( n \) and \( m \).

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