
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
With the popularization of the concept of "low-carbon living, green travel," new energy vehicles are gradually becoming people's favorite means of transportation. A certain 4S dealership plans to purchase a batch of new energy vehicles for sale. It is known that purchasing 3 units of type A new energy vehicles and 2 units of type B new energy vehicles costs a total of 95 million yuan; purchasing 4 units of type A new energy vehicles and 1 unit of type B new energy vehicle costs a total of 110 million yuan.  
$(1)$ What is the purchase price per unit for type A and type B new energy vehicles, respectively?  
$(2)$ If the company plans to purchase exactly 2.5 million yuan worth of the two types of new energy vehicles (both types of vehicles are purchased), and selling 1 unit of type A vehicle yields a profit of 12,000 yuan, and selling 1 unit of type B vehicle yields a profit of 8,000 yuan, if all these new energy vehicles are sold, how many different purchasing plans does the company have? What is the maximum profit in million yuan?

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