
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 probability of an event occurring in each of 100 independent trials is constant and equal to $p=0.8$. Find the probability that the event will occur: 

a) at least 75 times and no more than 90 times; 

b) at least 75 times; 

c) no more than 74 times.

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