
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
The traffic police brigade of our county is carrying out a comprehensive road traffic safety rectification campaign "Hundred-Day Battle" throughout the county, which strictly requires riders of electric bicycles and motorcycles to comply with the rule of "one helmet, one belt". A certain dealer purchased a type of helmet at a unit price of $30. When the selling price is $40, the monthly sales volume is 600 units. On this basis, for every $1 increase in the selling price, the monthly sales volume will decrease by 10 units. In order for the dealer to achieve a monthly profit of $10,000 from selling this helmet and to minimize inventory as much as possible, what should be the actual selling price of this brand of helmet? Explain your reasoning.

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