
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
Zibo barbecue is famous throughout China. A specialty barbecue restaurant hopes to make good profits during the National Day holiday. After calculation, the cost of lamb skewers is $3$ yuan per skewer. Drawing on past experience, if each skewer is sold for $10$ yuan, on average, they can sell 300 skewers per day. If the price is reduced by $0.5$ yuan, they can sell an additional 30 skewers per day. <br/>$(1)$ If the small shop sells at least 360 skewers per day, what is the maximum price per skewer for the lamb skewers? <br/>$(2)$ In order to maintain the image of Zibo barbecue, it is stipulated that the price per skewer must not exceed $8$ yuan. At what price per skewer can the store make a profit of $1920$ yuan per day?

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