
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
Linxian pomegranate is a long-standing variety of pomegranate, loved by many for its plump seeds, sweet taste, bright color, and pleasant fragrance. A fruit merchant purchased a batch of Linxian pomegranates at a price of $2$ yuan per pound, and then sold them at a price of $6$ yuan per pound, with an average daily sales of $150$ pounds. Upon investigation, it was found that if the price of pomegranates is reduced by $0.5$ yuan per pound, the average daily sales would increase by $50$ pounds. In order to reduce inventory quickly, the fruit merchant decided to reduce the price for sale.<br/>$(1)$ If the price of pomegranates is reduced by $x$ yuan per pound, the daily sales volume will be ______ pounds; (express using an algebraic expression with $x$)<br/>$(2)$ If the fruit merchant needs to ensure a daily profit of $750$ yuan from the sale of pomegranates, how much should the price of pomegranates be reduced per pound?

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