
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  $\displaystyle{2n}$  students in a school  $\displaystyle{\left( {n \in {\Bbb N},n \geqslant 2} \right)}$ . Each week  $\displaystyle{n}$  students go on a trip. After several trips the following condition was fulfiled: every two students were together on at least one trip. What is the minimum number of trips needed for this to happen?

*Proposed by Oleksandr Rybak, Kiev, Ukraine.*

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