
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 Spring Festival, a supermarket holds a promotional lottery event. When the amount spent by a customer reaches a certain threshold, they can participate in a lottery. The rules of the event are: from a box containing 3 black balls, 2 red balls, and 1 white ball (identical except for color), customers can draw balls.
(Ⅰ) If the customer spends more than 100 yuan but no more than 500 yuan, they can draw 2 balls at once. Each black ball drawn is rewarded with 1 yuan in cash, each red ball is rewarded with 2 yuan in cash, and each white ball is rewarded with 3 yuan in cash. Calculate the probability that the total reward money is at least 4 yuan.
(Ⅱ) If the purchase amount exceeds 500 yuan, they can draw twice from the box, drawing one ball each time and then returning it before drawing again. Each black ball and white ball drawn is rewarded with 5 yuan in cash, and each red ball is rewarded with 10 yuan in cash. Calculate the probability that the total reward money is less than 20 yuan.

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