
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 Public Security Traffic Police Department reminds citizens that when riding a bicycle, they must strictly adhere to the rule of "one helmet, one belt." A helmet dealer has compiled the sales data of a certain brand of helmets from April to June. The brand sold 150 helmets in April and 216 helmets in June, with the monthly growth rate of sales being the same from April to June.  
$(1)$ Find the monthly growth rate of sales for this brand of helmets.  
$(2)$ If the cost price of this type of helmet is $30$ yuan per helmet, and it is estimated that in the market, when the selling price is $40$ yuan per helmet, the monthly sales volume is 600 helmets. If with each increase of $1$ yuan per helmet, the monthly sales volume decreases by 10 helmets, in order to achieve a monthly sales profit of $10,000$ yuan and to provide customers with the best value, what should be the actual selling price per helmet for this brand of helmets?

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