
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
A sales company went to a certain car manufacturing company to purchase two models of cars, $A$ and $B$. With 3 million yuan, they can buy 10 cars of model $A$ and 15 cars of model $B$; with 3 million yuan, they can buy 8 cars of model $A$ and 18 cars of model $B.  
$(1)$ Find the price of each car of models $A$ and $B$.  
$(2)$ If the car sales company can earn 8000 yuan by selling one car of model $A$ and 5000 yuan by selling one car of model $B, and the company is prepared to buy a total of 30 cars of models $A$ and $B for no more than 4 million yuan, and after selling all these cars, the total profit is not less than 204,000 yuan, how many purchasing plans are there? Among these plans, which one yields the highest profit?

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