
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
Let \( m \) and \( n \) be two natural numbers. A school has \( n \) students dining in the cafeteria. During the year, the cafeteria offered 100 different dishes. Each student tasted 10 different dishes. Furthermore, for any two dishes among the 100, exactly \( m \) students tasted both dishes. Calculate the ratio: \( \frac{n}{m} \).

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