
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 certain new product in a shopping mall has a cost price of 120 yuan per item. During the trial sale period, it was found that when the price of each item is set at 130 yuan, 70 items can be sold per day. When the price of each item is higher than 130 yuan, for every 1 yuan increase in price, the daily sales volume decreases by 1 item. Based on this rule, please answer:
(1) When the price of each item is set at 140 yuan, how many items can be sold per day? What is the daily profit of the mall?
(2) Under the same conditions and assuming normal sales of the product, what should be the selling price per item for the mall to achieve a daily profit of 1500 yuan?
(3) At what price per item should the merchant set to achieve the maximum profit, and what is the profit at this price?

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