
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
Xiangshan is known as the "hometown of Chinese citrus fruits." Recently, the operator Lao Zhang mainly sells two varieties of citrus fruits, "Red Beauty" and "Xiangshan Green."

$(1)$ Last week, the purchase price and selling price of "Red Beauty" and "Xiangshan Green" are shown in the table below. Lao Zhang wholesaled a total of 300 kilograms of "Red Beauty" and "Xiangshan Green" for $3000. After selling them all last week, how much money did he earn in total?

|            | Red Beauty | Xiangshan Green |
|------------|------------|-----------------|
| Purchase Price (yuan/kg) | $20 | $5 |
| Selling Price (yuan/kg) | $35 | $10 |

$(2)$ This week, keeping the purchase price unchanged, Lao Zhang still wholesaled a total of 300 kilograms of "Red Beauty" and "Xiangshan Green" for $3000. However, during transportation, 10% of the "Red Beauty" was damaged, while the "Xiangshan Green" was not damaged and was sold at the original price. In order for the profit after selling this week not to be lower than last week's profit, what should be the minimum selling price of "Red Beauty"? (Round to $0.1$ yuan)

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