
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 shopping mall launched a double lottery event, where purchasing goods of a certain value grants a lottery ticket. The ticket has a redemption code that can participate in two identical lottery events. If the probability of winning in both lottery events is 0.05, calculate the probability of the following events in the two lotteries:  
(1) Winning a specific number in both lotteries;  
(2) Winning a specific number exactly once in the two lotteries;  
(3) Winning a specific number at least once in the two lotteries.

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