
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
The "Sunshine Rose" grapes have been widely favored by consumers in various regions in recent years and are widely planted in Yunnan Province. A fruit distributor purchases a batch of "Sunshine Rose" grapes at a price of $15$ yuan per kilogram. If sold at a price of $30$ yuan per kilogram, an average of $60$ kilograms can be sold per day. Combining sales records, it is found that if the selling price is reduced by $1$ yuan, the average daily sales volume increases by $10 kilograms. In order to reduce inventory quickly, the fruit distributor decides to reduce the price for sale.<br/>$(1)$ If the price is reduced by $2$ yuan at a time, the daily sales profit is ______ yuan;<br/>$(2)$ When the selling price per kilogram is set at how many yuan, the profit obtained from selling Sunshine Rose grapes per day is maximized? What is the maximum profit in yuan?

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