
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
While tidying up the children's room before guests arrived, a mother found nine socks. Among any four of these socks, at least two belonged to the same child, and among any five, no more than three belonged to the same child. How many children could there be, and how many socks could belong to each child?

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