
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
This year, Dafu Supermarket purchased a batch of goods at a cost of $25$ yuan each. When the selling price of the goods is $40$ yuan, they sold $256$ items in March. The sales of the goods were very good in April and May, with sales continuing to rise. With the selling price unchanged, the sales volume in April and May reached $400$ items.<br/>$(1)$ Find the average monthly growth rate for April and May.<br/>$(2)$ Starting from June, in order to reduce inventory, the supermarket adopted a promotional strategy of reducing prices. After investigation, it was found that for every $1$ yuan reduction in price of the goods, the monthly sales volume increased by $5$ items. How much should the price be reduced for the supermarket to earn $4250$ yuan per month?

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