
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 National Day holiday, a shopping mall plans to hold a sales promotion based on market research. The mall decides to choose 3 items for the promotion from among 2 kinds of clothing, 2 kinds of home appliances, and 3 kinds of daily necessities.

(1) Calculate the probability that at least one of the 3 chosen items is a daily necessity.
(2) For the chosen item, the promotion scheme adopted by the mall is prize-selling: the price of the item is increased by 150 yuan, and if a customer buys the item, they get 3 chances to draw a lottery. If they win, they will receive a cash prize of m yuan for each win. Assuming that the probability of winning the lottery each time is $\frac{1}{2}$, what is the maximum amount of m that the mall can set for each cash prize to ensure that the promotion scheme is favorable for the mall?

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