
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
A certain store purchased a batch of goods at a cost of $25$ yuan per item at the beginning of this year. When the selling price of the goods was $40$ yuan, 256 items were sold in January. The sales of the goods were very good in February and March, with sales continuing to increase. With the selling price unchanged, the sales volume in March reached 400 items. It is assumed that the average monthly growth rate in February and March remains the same.
  
$(1)$ The average monthly growth rate in February and March is ______%. (Fill in the result directly)  
$(2)$ Starting from April, the store decided to use price reductions to promote sales and reward customers. After investigation, it was found that for every $1$ yuan reduction in price of the goods, the sales volume increased by 5 items. How much should the price be reduced for the store to make a profit of $4250$ yuan in that month?

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