
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 sells a desk lamp with a cost price of $25$ yuan for $40$ yuan. The sales in January were 256 units, and the sales continued to increase in February and March. In March, the sales reached 400 units at the same selling price. <br/>$(1)$ Find the monthly average growth rate of sales for February and March. <br/>$(2)$ The store decides to reduce the price for promotion starting from April. After investigation, it was found that for every $1$ yuan reduction in the lamp price from March, the sales volume would increase by 4 units. If the store wants to make a profit of $4200$ yuan from selling this type of lamp in April, what should be the selling price of the lamp?

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