
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 fruit store sells a type of fruit. When the price is set at $58$ yuan per box, they can sell $300$ boxes per week. It is found that for every $1$ yuan decrease in price per box, they can sell an additional $25$ boxes per week, and for every $1$ yuan increase in price, they will sell $10$ boxes less per week. It is known that the cost price per box of fruit is $35$ yuan, and the average loss cost per box per week is $3$ yuan.  
$(1)$ If there is no price adjustment, what is the weekly sales profit of this type of fruit?  
$(2)$ Based on the above information, how should the price be set to maximize the weekly sales profit of this type of fruit?

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