
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
A teacher asked each student in a class to write down the number of classmates with the same surname as his, as well as the number of classmates whose birthday is the same as his. Among the answers received, each of the numbers 0, 1, 2, ..., 10 has appeared. Find the minimum number of students in the class.

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