
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
There are 60 students in a conference room. It is known that among any 10 students, there are at least 3 students who are from the same class. Is it necessarily true that among these 60 students, there are at least 15 students from the same class? Is it necessarily true that among these 60 students, there are at least 16 students from the same class?

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