
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 shop sells a product that cost them 100 yuan at a price of 120 yuan, and they can sell 300 units at this price. For every 1 yuan increase in price beyond 120 yuan, they sell 10 fewer units, and for every 1 yuan decrease in price, they sell 30 more units.  
(1) If the price of the product is increased by x yuan from the base price of 120 yuan, determine the functional relationship between the profit obtained, $y_1$ (in yuan), and the price increase, x (in yuan).  
(2) If the price of the product is decreased by x yuan from the base price of 120 yuan, determine the functional relationship between the profit obtained, $y_2$ (in yuan), and the price decrease, x (in yuan).  
(3) To maximize profit, what should the store set the price at?

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