
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
Two satellites, A and B, monitor a typhoon independently at the same time. The probabilities of A and B correctly forecasting the typhoon are $\frac{4}{5}$ and $\frac{3}{4}$, respectively. During this time period, find: 
(I) The probability that both A and B forecast the typhoon correctly;
(II) The probability that at least one satellite forecasts the typhoon correctly;
(III) The probability that satellite A makes 4 independent forecasts and exactly 3 of them are correct.

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