
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
June 5th is World Environment Day every year. In order to promote low-carbon environmental protection, a company decides to purchase 10 energy-saving new devices. There are two models, A and B, available for purchase. After investigation, it is found that buying 3 A-type devices costs $16,000 more than buying 2 B-type devices, and buying 2 A-type devices costs $6,000 less than buying 3 B-type devices.  
$(1)$ Find the prices of the A and B type devices.  
$(2)$ The company has budgeted to purchase energy-saving new devices with a total cost not exceeding $110,000. What are the possible purchasing plans for the company?  
$(3)$ Under the condition in $(2)$, given that the production capacity of A-type devices is 240 tons per month and the production capacity of B-type devices is 180 tons per month, if the total production capacity per month should not be less than 2040 tons, in order to save money, design the most cost-effective purchasing plan for the company.

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