
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 held a promotional event where customers could participate in a lottery if their purchase amount reached a certain level. The rules of the event were as follows: draw balls from a box containing 3 black balls, 2 red balls, and 1 white ball (the balls are identical except for their color).  
(Ⅰ) When the purchase amount exceeds 100 yuan but does not exceed 500 yuan, customers can draw 2 balls from the box at once. For each black ball drawn, a cash reward of 1 yuan is given; for each red ball, a cash reward of 2 yuan is given; and for each white ball, a cash reward of 3 yuan is given. Calculate the probability that the reward amount is not less than 4 yuan.  
(Ⅱ) When the purchase amount exceeds 500 yuan, customers can draw from the box twice, drawing one ball each time and then putting it back before drawing again. For each black ball and white ball drawn, a cash reward of 5 yuan is given; for each red ball, a cash reward of 10 yuan is given. Calculate the probability that the reward amount is less than 20 yuan.

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