
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 youth radio station, to attract listeners' attention, gives away gifts and grand prizes among them. Gifts are given away hourly over sixteen hours (one gift per hour), and grand prizes are given away during four evening hours (one grand prize per hour). The probability that listeners win a prize is 0.3, and a grand prize is 0.02.

Find the probability that over 30 days:

a) Listeners will win three grand prizes;

b) Listeners will win between 130 to 160 prizes.

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