
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 certain car trading company sells two models of electric cars, $A$ and $B$. The company earns a profit of $34,000 yuan by selling 3 cars of model $A$ and 2 cars of model $B$, and a profit of $28,000 yuan by selling 1 car of model $A$ and 4 cars of model $B$. <br/>$(1)$ Find the profit per car for models $A$ and $B$ in thousand yuan. <br/>$(2)$ If the purchase price for model $A$ is 160,000 yuan per car and for model $B$ is 140,000 yuan per car, and the company plans to use no more than 4,400,000 yuan to purchase a total of 30 new energy cars of models $A$ and $B$, with a profit of at least 177,000 yuan, how many cars of model $A$ and model $B$ should be purchased?

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