
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
90 students arrived at the camp. It is known that among any 10 students, there will always be two friends. A group of students is said to form a friendship chain if the children in the group can be numbered from 1 to \(k\) such that all the students can be divided into no more than 9 groups, each of which forms a friendship chain. (A group of one student also forms a friendship chain.)

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