
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 order to strictly control the quality of fruits, a certain orchard has established strict fruit standards. The Red Fuji apples planted in the orchard are divided into 18 grades based on "sugar acidity, freshness, tenderness, fragrance, and safety". Grade 1 Red Fuji has the best quality, followed by Grade 2, and so on, with Grade 18 having the worst quality. When selling Red Fuji apples, the orchard sets the following prices: the price of Grade 9 Red Fuji is $16$ yuan per kilogram. Starting from Grade 9, for each increase in quality level, the price per kilogram will increase by $0.5$ yuan; for each decrease in quality level, the price per kilogram will decrease by $0.4$ yuan. 

$(1)$ If the grade of Red Fuji is $n$, express the price of that grade using an algebraic expression containing $n$ (unit: yuan per kilogram):
① When $n \lt 9$, the price is ______ yuan per kilogram;
② When $n \gt 9$, the price is ______ yuan per kilogram;
$(2)$ The fruit shop owner Xiao Bei plans to purchase $300$ kilograms of Grade 5 Red Fuji from the orchard. The orchard is responsible for delivering the goods to her door, but charges $200$ yuan for delivery. Since Xiao Bei is a loyal customer of the orchard, the orchard manager has provided the following two discount options:
Option 1: 5% discount and waiver of all delivery charges;
Option 2: 8% discount, but no reduction in delivery charges.
Please help Xiao Bei calculate which discount option is more cost-effective.

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