
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
When a polio vaccine is administered, immunity is created in $99.99\%$ of cases. What is the probability that out of 1000 vaccinated children, respectively, $1, 2, 3,$ or $4$ children will get sick?

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