
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
On September 22, 2020, the Chinese government proposed at the 75th United Nations General Assembly: "China will increase its national determined contributions, adopt more effective policies and measures, strive to peak carbon dioxide emissions before 2030, and endeavor to achieve carbon neutrality before 2060. "Low-carbon transportation" is one of the measures to achieve "carbon neutrality", and the purchase of new energy vehicles lays a good foundation for a "low-carbon" earth. A certain car trading company sells two models of new energy vehicles, $A$ and $B$. Selling 2 units of model $A$ and 7 units of model $B$ can generate a profit of 41,000 yuan, while selling 1 unit of model $A$ and 3 units of model $B$ can generate a profit of 18,000 yuan. <br/>$(1)$ Find the profit from selling one unit of model $A$ and one unit of model $B$. <br/>$(2)$ The company plans to purchase a total of 30 units of models $A$ and $B$, with a profit of at least 131,000 yuan. How many units of model $B$ should be purchased at least?

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