
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
To protect the environment, the public transportation company in our county plans to purchase two types of environmentally friendly and energy-saving buses, type A and type B, totaling 10 buses. If they buy 1 type A bus and 3 type B buses, it will cost a total of 380 million yuan; if they buy 2 type A buses and 2 type B buses, it will cost a total of 360 million yuan.  
$(1)$ Find out how much each type A and type B bus costs.  
$(2)$ It is estimated that on a certain route, type A and type B buses can each carry an average of 500,000 and 600,000 passengers per year, respectively. If the total cost of purchasing type A and type B buses does not exceed 880 million yuan, and it is ensured that the total annual passenger volume of these 10 buses on this route is not less than 5.2 million, what are the possible purchasing plans for the company?  
$(3)$ Under the conditions of $(2)$, which purchasing plan incurs the least total cost? What is the minimum total cost in million yuan?

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