
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
Based on past statistics, the probability of a car owner in a certain area purchasing insurance type A is 0.5, and the probability of purchasing insurance type B but not insurance type A is 0.3. Assume that each car owner's insurance purchase is independent.  
(I) Calculate the probability that a car owner in that area purchases at least one of the two types of insurance, A or B.  
(II) Calculate the probability that exactly one out of three car owners in that area does not purchase either insurance A or B.

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