
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
Suppose the probability of each customer entering a certain shopping mall buying product A is 0.5, and the probability of buying product B is 0.6. Moreover, the purchase of product A and product B are independent of each other, and the purchases made by different customers are also independent.  
(1) Calculate the probability of a customer entering the mall buying only one of the products A or B.  
(2) Calculate the probability that among 3 customers entering the mall, at least 2 customers neither buy product A nor product B.

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