
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
(2012•Shenhe District Mock) A store sells a product, which costs 100 yuan to purchase, at a price of 120 yuan, and can sell 300 units at this price. If the store increases the price by 1 yuan from 120 yuan, it will sell 10 fewer units, and for every 1 yuan decrease in price from 120 yuan, it will sell 30 more units.  
(1) Find the function relationship between the profit $y$ (in yuan) and the selling price $x$ (in yuan);  
(2) To maximize profit, what should the selling price be?  
(3) To benefit the customers while keeping the profit the same, please choose the correct selling method for the store and calculate the selling price at this time.

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