
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
In recent years, more and more businesses have been transforming and developing towards the internet. "Livestreaming sales" has become an important way for businesses to sell products. A certain business sells a daily commodity in a livestream room with a cost price of $10$ dollars per item. Through investigation, it is found that the daily sales quantity $y$ (in items) of the product is related to the selling price $x$ (in dollars) by the equation $y=-10x+300$. Let $W$ (in dollars) be the profit of selling this product per day.
  
$(1)$ If the business wants to make a profit of $750$ dollars per day, what should the selling price be set at?
  
$(2)$ Find the maximum value of the profit $W$ per day.

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