
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 store sells a certain product, with an average daily sales of 20 items and a profit of $40 per item. In order to expand sales and increase profits, the store has implemented a price reduction measure. After a period of sales, it was found that for every $1 decrease in the selling price, the store can sell an additional 2 items per day, with the condition that the profit per item is not less than $25. Given this scenario:
- $(1)$ If the price is reduced by $a$ dollars, the average daily sales will be ______ items (expressed as an algebraic expression involving $a$).
- $(2)$ How much should the price of each item be reduced by for the store to make a daily profit of $1200 dollars?

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