
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 200 candies. What is the minimum number of schoolchildren that these candies can be distributed to so that, no matter how the candies are distributed, there are always at least two schoolchildren who receive the same number of candies (possibly none)?

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