
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
The participants of the olympiad left 9 pens in the room. Among any four pens, at least two belong to the same person. And among any five pens, no more than three belong to the same person. How many students forgot their pens, and how many pens does each student own?

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