
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 math comprehensive practice group from Class 2 of Grade 9 of a certain school went to Walmart to investigate the sales of a certain product during the "Ten times One" period. The following is the conversation between Xiao Yang and two other classmates after the investigation: Xiao Yang: According to the investigation, the cost price of the product is $12 per item. Xiao Jia: When the product is priced at $20, 240 items can be sold per day. Xiao Xin: On the basis of the price of $20, for every $1 reduction in price, an additional 40 items are sold per day. If the supermarket wants to reduce inventory for promotion and make a profit of $1920 per day from selling the product, according to their conversation, complete the following questions:  
$(1)$ If the profit from selling the product per day is $1920, how much should the price be reduced by to be more reasonable?  
$(2)$ When $x$ takes what value, the supermarket makes the maximum profit from selling this product, and what is the maximum profit?

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