
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
500 products manufactured at a plant, where defects account for $2\%$, are being examined. Find the probabilities that: 
1) Exactly 10 of them are defective;
2) The number of defective items is between 10 and 20.

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