
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
Live shopping is gradually becoming a part of people's lives. An e-commerce platform is selling a small item with a cost price of $40$ yuan through live streaming on Douyin. If each item is sold for $60$ yuan, they can sell $20$ items per day. Through market research, it is found that for each $5$ yuan decrease in the selling price of the item, the daily sales volume increases by $10$ items. If the selling price of each item is set to $x$ yuan and the daily sales volume is set to $y$ items, find:<br/>$(1)$ The function expression of $y$ in terms of $x$;<br/>$(2)$ For what value of $x$ is the daily sales profit maximized? What is the maximum profit?

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