
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 have become the preferred mode of transportation for most people. A public transportation company in a certain city purchased a batch of two models of new energy vehicles, $A$ and $B$. It is known that purchasing 3 $A$ type cars and 1 $B$ type car requires a total of 85 million yuan, and purchasing 2 $A$ type cars and 4 $B$ type cars requires a total of 140 million yuan.  
$(1)$ Find out how much each $A$ type and $B$ type car costs to purchase.  
$(2)$ If the company plans to purchase a total of 15 $A$ and $B$ type cars, and the number of $A$ type cars does not exceed twice the number of $B$ type cars, provide the most cost-effective purchasing plan, determine the minimum cost, and explain the reasoning.

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