
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 is holding a prize promotion event, where customers can participate in a lottery after purchasing a certain amount of goods. For each lottery draw, one ball is randomly drawn from each of the two boxes: Box A, which contains 4 red balls and 6 white balls, and Box B, which contains 5 red balls and 5 white balls. If both drawn balls are red, the customer wins the first prize; if only one of the drawn balls is red, the customer wins the second prize; if no red balls are drawn, the customer does not win a prize.
(1) Calculate the probability that a customer wins a prize in one lottery draw.
(2) If a customer has 3 chances to participate in the lottery, calculate the probability that the customer wins the first prize at most twice in these 3 draws.

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