
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
Summer is coming, and the sales of air conditioners are entering the peak season. A certain appliance supermarket sells two models of air conditioners, $A$ and $B$. The revenue from selling 3 units of model $A$ and 5 units of model $B$ is 23500 yuan, and the revenue from selling 4 units of model $A$ and 10 units of model $B$ is 42000 yuan.  
$(1)$ Find the unit selling prices of models $A$ and $B$.  
$(2)$ If the cost price of each unit of model $A$ is 1800 yuan and each unit of model $B$ is 2400 yuan, and the supermarket plans to purchase a total of 50 units of these two models, making a profit of at least 38000 yuan after selling all units, how many units of model $B$ at least need to be purchased?

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