
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 large supermarket purchased a popular disinfectant laundry detergent. Due to the rise in raw material prices, the cost price per bottle of detergent this year increased by $4$ compared to last year. The quantity of detergent purchased for $1440$ yuan this year is the same as the quantity purchased for $1200$ yuan last year. When the selling price per bottle of detergent is $36$ yuan, the supermarket can sell 600 bottles per week. In order to increase sales, the supermarket decides to reduce the price. Market research shows that for every $1$ reduction in price, the weekly sales volume can increase by 100 bottles. It is stipulated that the selling price of this disinfectant laundry detergent should not be lower than the cost price.<br/>$(1)$ Find the cost price per bottle of this disinfectant laundry detergent this year;<br/>$(2)$ When the selling price per bottle of this disinfectant laundry detergent is set at how much, the weekly sales profit of this detergent is maximized? What is the maximum profit in yuan?

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