
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 three classes, each with \( n \) students, and all \( 3n \) students have different heights. These students are grouped into \( n \) groups, with each group consisting of 3 students from different classes. The tallest student in each group is called the "tall one". It is known that no matter how the groups are formed, each class has at least 10 "tall ones". Determine the smallest possible value of \( n \).

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