
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 store sells a batch of helmets for $80 each. It can sell 200 helmets per month. During the "Creating a Civilized City" period, the store plans to reduce the price of the helmets for sale. After investigation, it was found that for every $1 decrease in price, an additional 20 helmets are sold per month. It is known that the cost price of the helmets is $50 each.  
$(1)$ If the price of each helmet is reduced by $10, the store can sell ______ helmets per month, and the monthly profit from sales is ______ dollars.  
$(2)$ If the store plans to reduce the price of these helmets to reduce inventory while ensuring a monthly profit of $7500, find the selling price of the helmets.

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