
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 the occurrence of an event 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 70 and at most 85 times; 
b) at least 70 times; 
c) at most 69 times.

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