
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
During the "Golden Week" of this year's National Day, a shopping mall adopted a shopping lottery promotion method (each person can only participate in the lottery once), setting up gold and silver prizes with a total of 2000 lottery tickets. During a certain period, a survey was conducted among 30 customers, among whom $$\frac {2}{3}$$ of the customers did not win any prize, and among the winning customers, $$\frac {3}{5}$$ won the silver prize. If 3 customers are randomly interviewed from these 30 customers:  
(1) Calculate the probability that at least one of the 3 selected customers won the gold prize;  
(2) Calculate the probability that the number of customers who won the gold prize among the 3 selected customers is not more than the number of customers who won the silver prize.

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