
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 tenth anniversary of a large shopping mall, a prize sale is organized to thank customers. During the prize sale period, customers get a chance to enter a lottery for each purchase of 100 yuan worth of goods from the mall, with the opportunity to win corresponding prizes if they win. The lottery scheme is as follows: 2 balls are drawn from a box containing 3 red balls labeled A, B, C and 3 white balls with the label f'(x₀)=0. If both drawn balls are red, a first prize is won; if exactly one red ball is drawn, a second prize is won; otherwise, no prize is awarded. Apart from color and label, the balls in the box are identical.  
(Ⅰ) If a customer enters the lottery once, calculate the probability of winning the first prize.  
(Ⅱ) If a customer enters the lottery once, calculate the probability of winning a prize.

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