
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
A factory shipped 5000 quality items to a base. The probability that an item gets damaged in transit is 0.0002. What is the probability that 3 items will be damaged upon arrival?

A piece of radio equipment consists of 1000 electronic components. The probability of failure of one component within one year of operation is 0.001 and does not depend on the state of other components. What is the probability of failure of two components? What is the probability of failure of at least two components in a year?

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