
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 the Chinese lunar calendar, the year 2023 is the year of the Rabbit. Before the Spring Festival, a purchasing officer in a shopping mall plans to purchase two types of cloth rabbits, "Lucky Rabbit" and "Auspicious Rabbit." It is found that the quantity of "Lucky Rabbit" purchased for 8800 yuan is twice the quantity of "Auspicious Rabbit" purchased for 4000 yuan, and the cost price of each "Lucky Rabbit" is 4 yuan more expensive than the cost price of each "Auspicious Rabbit."  
$(1)$ What are the cost prices of each "Lucky Rabbit" and "Auspicious Rabbit" respectively?  
$(2)$ To meet consumer demand, the supermarket is preparing to purchase a total of 200 "Lucky Rabbit" and "Auspicious Rabbit." The selling price of "Lucky Rabbit" is set at 70 yuan, and the selling price of "Auspicious Rabbit" is 60 yuan. If the total profit is not less than 4120 yuan, what is the minimum number of "Lucky Rabbit" to be purchased?

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