
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 store sells a batch of branded shirts, with an average daily sale of 20 pieces, making a profit of 40 yuan per piece. To expand sales, increase profits, and reduce inventory as much as possible, the store decided to take appropriate price reduction measures. It was found through investigation that for every 1 yuan reduction in the price of each shirt, the store could sell an additional 2 pieces per day;  
(1) If the store wants to make an average daily profit of 1,200 yuan, by how much should the price of each shirt be reduced?  
(2) When the price of each shirt is reduced by how much, does the store make the maximum average daily profit?

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