
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
Students from three different classes participate in a hike. The instructor conducting the hike does not know which class each student belongs to. What is the minimum number of duty students that he must appoint so that among them there are:
1) at least two students from the same class;
2) at least three students from the same class?

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