
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 March to May. The brand sold 256 helmets in March and 400 helmets in May, with the monthly growth rate of sales from March to May being $r\left(r \gt 0\right)$.  
$(1)$ Find the monthly growth rate $r$;  
$(2)$ After conducting a market survey, it was found that if the cost price of this type of helmet is $30$ yuan per helmet, and the selling price is $40 yuan per helmet, the monthly sales volume is 600 helmets. If the selling price increases by $1$ yuan per helmet, the monthly sales volume will decrease by 10 helmets. In order to achieve a monthly sales profit of 10,000 yuan and to make customers feel that they are getting a good deal, what should be the actual selling price per helmet for this brand of helmet?

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