
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 Changsha Municipal Government has introduced a series of preferential policies for "rural revitalization strategy," which has significantly increased the income of farmers. A farmer produces and sells a certain agricultural product. It is known that the cost price of this agricultural product is $20 per kilogram. Through market research, it is found that the daily sales quantity $y$ (in kilograms) of this agricultural product has the following relationship with the selling price $x$ (in dollars per kilogram): $y=-2x+80$. Let $W$ be the daily sales profit of this agricultural product.
$(1)$ Find the functional relationship between $W$ and $x$;
$(2)$ If the price department stipulates that the selling price of this agricultural product should not exceed $30 per kilogram, and the farmer wants to make a daily sales profit of $150, what should be the selling price per kilogram?

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