
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 40 pencils of four different colors, 10 pencils of each color. These pencils are distributed among 10 children, with each child receiving 4 pencils. What is the minimum number of children that can always be selected to ensure that they collectively have pencils of all colors, regardless of the distribution of the pencils?

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