
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
A customer entering a shopping mall has a probability of $0.5$ of purchasing product A and a probability of $0.6$ of purchasing product B. The purchase of product A and product B are independent events, and the purchases made by different customers are also independent.

1. Find the probability that a single customer purchases either product A or product B.
2. Find the probability that a single customer purchases at least one of the products A or B.
3. Let $ξ$ denote the number of customers among 3 who purchase at least one of the products A or B. Determine the probability distribution of $ξ$.

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