
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]


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With the development of new energy vehicles, a bus company plans to replace the fuel buses emitting heavy black smoke on a certain route with new energy buses. They plan to purchase a total of 10 new energy buses of type $A$ and type $B$. If purchasing 1 bus of type $A$ and 2 buses of type $B$ costs a total of 300 million yuan, and purchasing 2 buses of type $A$ and 1 bus of type $B$ costs a total of 270 million yuan.<br/>$(1)$ Find out how much each bus of type $A$ and type $B$ costs?<br/>$(2)$ If the total cost of purchasing type $A$ and type $B$ buses does not exceed 1000 million yuan, how many buses of type $A$ does the company need to purchase at least? What is the total cost of purchasing type $A$ and type $B$ buses in this case?

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