
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 promote the clean and low-carbon transformation in industries, construction, transportation, and other fields, a certain city's transportation management bureau decided to purchase a batch of electric buses to replace fuel buses. According to the investigation, the unit price of type $A$ electric buses is $4$ million yuan less than the unit price of type $B$ electric buses. The quantity of type $A$ electric buses that can be purchased with $720$ million yuan is the same as the quantity of type $B$ electric buses that can be purchased with $800$ million yuan.
$(1)$ What are the unit prices of type $A$ and type $B$ electric buses in million yuan?
$(2)$ The transportation management bureau plans to purchase a total of $30$ electric buses, with the quantity of type $A$ electric buses being no less than $10$ and no more than twice the quantity of type $B$ electric buses. Design the most cost-effective purchasing plan and explain the reasoning.

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