
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 store sells a product, which is purchased at a cost of 100 yuan, for 120 yuan, selling 300 units. For every 1 yuan increase in price above 120 yuan, 10 fewer units are sold; on the other hand, for every 1 yuan decrease in price, 30 more units are sold.  
(1) Determine the function that describes the relationship between the profit $y$ (in yuan) and the selling price $x$ (in yuan);  
(2) To maximize profit, what should the store set the price at?  
(3) To favor customers while maximizing profit, what should the store set the price at?

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