
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 cleaning the children's room in anticipation of guests, a mom found 9 socks. Among any four socks, at least two belong to the same child. Additionally, among any five socks, no more than three belong to the same child. How many children scattered the socks and how many socks belong to each child?

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