
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 supermarket purchased a batch of fruits at a cost of $25$ yuan per box. When the selling price of the fruit is $40$ yuan per box, they sold $256$ boxes in June. The sales continued to rise in July and August, with the sales reaching $400$ boxes in August while keeping the selling price constant.<br/>$(1)$ Find the monthly average growth rate for July and August.<br/>$(2)$ In September, the supermarket started a price reduction promotion to reduce inventory. After investigation, it was found that for every box of fruit that was reduced by $1$ yuan, the monthly sales increased by $5$ boxes compared to August. How much should the price be reduced per box so that the supermarket can make a profit of $4250$ yuan in September?

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