
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 department store sells a batch of branded shirts, with an average daily sale of 20 pieces, making a profit of 40 yuan per piece. To increase sales, the store decides to implement appropriate price reductions. It has been found through investigation that if the price of each shirt is reduced by 1 yuan, the store can sell an additional 2 pieces per day.

(1) If the store wants to make an average daily profit of 1200 yuan, by how much should the price of each shirt be reduced?

(2) To achieve the maximum profit, by how much should the price of each shirt be reduced? What is the maximum profit?

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