
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 promotional event where for every 500 yuan spent, customers can choose to either receive a 50 yuan cashback or participate in a lottery. The lottery rules are as follows: draw one ball from a box containing 6 white balls and 4 red balls. Drawing a red ball wins a 100 yuan cash prize. Assume the outcomes of the lottery draws are independent.  
(Ⅰ) If a customer chooses to participate in the lottery once, calculate the probability of winning a 100 yuan cash prize;  
(Ⅱ) A customer has spent 1500 yuan. As the manager of the mall, would you prefer the customer to choose the 150 yuan cashback directly or to participate in the lottery three times? Explain your reasoning;  
(Ⅲ) If a customer participates in the lottery 10 times, what is the most likely amount of cash prize they will win?

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