
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 statistical data, 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 type A is 0.3. Assume that each car owner's insurance purchase is independent.
(Ⅰ) Find the probability that one car owner in that area purchases at least one of the two types of insurance, A or B.
(Ⅱ) Let X represent the number of car owners out of 100 in that area who do not purchase either insurance type A or B. Find the expected value of X.

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