
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 supermarket sells a batch of down jackets, with an average daily sale of 20 pieces and a profit of 40 yuan per piece. To increase sales and profits, the supermarket decides to reduce the price appropriately. If the price of each down jacket is reduced by 1 yuan, an average of 2 more pieces can be sold per day. If the supermarket wants to ensure an average daily profit of 1200 yuan while also providing benefits to customers, how much should the price of each down jacket be reduced?

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