
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. Each lottery draw involves randomly picking 2 balls from a box A containing 4 red balls and 6 white balls, and 2 balls from a box B containing 5 red balls and 5 white balls. Among the 4 balls drawn, if all are red, the customer wins the first prize; if there are only 3 red balls, the customer wins the second prize; if there are only 2 red balls, the customer wins the third prize; if there is only 1 red ball, the customer wins the fourth prize; if there are no red balls, the customer does not win a prize.
1. Calculate the probability of a customer winning the first prize in one lottery draw;
2. Calculate the probability of a customer winning the second prize in one lottery draw;
3. Calculate the probability of a customer winning a prize in one lottery draw.

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