
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 shopping mall sells a batch of children's toys, with an average daily sales of 20 items and a profit of 40 yuan per item. After investigation, it was found that for this type of toy, for every 1 yuan reduction in price, an average of 2 more items are sold per day. Let $x$ represent the price reduction per item.

$(1)$ After the price reduction, the profit per item is ______ yuan, and the average daily sales volume is ______ items. (Express using expressions containing $x$)

$(2)$ In order to expand sales and reduce inventory quickly, the shopping mall decides to implement a price reduction measure, but it needs to make a daily profit of 1200 yuan. How much should each item be reduced by?

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