
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
Lanxi Lianhua Supermarket purchased a batch of water-milled rice cakes at a cost of $40$ yuan each in early March this year. When the selling price of the rice cakes was $60$ yuan each, a total of $192$ pieces were sold in March. The sales volume of this batch of rice cakes continued to increase in April and May, with the sales volume reaching $300$ pieces in May while keeping the selling price unchanged.<br/>$(1)$ Find the monthly average growth rate of sales in April and May;<br/>$(2)$ Starting from June, based on the sales volume in May, Lianhua Supermarket decided to offer discounts to customers. After a market survey, it was found that if the price of each rice cake is reduced by $2$ yuan, the monthly sales volume will increase by 40 pieces. To ensure that the customers get the maximum benefit, how much should the price of each rice cake be reduced by in June so that Lianhua Supermarket can still make a profit of $6080$ yuan?

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