
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
The factory sent 500 products to the base. The probability of a product being damaged during transit is 0.002. Find the probabilities that during transit: a) exactly three products will be damaged; b) fewer than three products will be damaged; c) more than three products will be damaged; d) at least one product will be damaged.

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