
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 accelerate the construction of public charging infrastructure, a certain parking lot plans to purchase two models of charging piles, denoted as $A$ and $B$. It is known that the unit price of type $A$ charging pile is $0.3$ million yuan less than that of type $B$ charging pile, and the quantity of type $A$ charging piles that can be purchased with $15$ million yuan is equal to the quantity of type $B$ charging piles that can be purchased with $20$ million yuan. <br/>$(1)$ What are the unit prices of the two types of charging piles, $A$ and $B$? <br/>$(2)$ The parking lot plans to purchase a total of $25$ type $A$ and type $B$ charging piles, with a total cost not exceeding $26$ million yuan, and the quantity of type $B$ charging piles purchased is not less than half of the quantity of type $A$ charging piles purchased. What are the possible purchasing schemes? Which scheme requires the least total cost?

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