
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 electrical appliance supermarket sells two models of electric fans, $A$ and $B$, with purchase prices of $210$ yuan and $180$ yuan per unit, respectively. The table below shows the sales situation over the past two weeks:

| Sales Period | Quantity of Model $A$ | Quantity of Model $B$ | Sales Revenue |
|--------------|-----------------------|-----------------------|---------------|
| Week 1       | 3 units               | 5 units               | $2150$ yuan   |
| Week 2       | 4 units               | 10 units              | $3700$ yuan   |

(Profit = Sales Revenue - Cost Price)

$(1)$ Find the selling prices of models $A$ and $B$.

$(2)$ If the supermarket is prepared to spend no more than $7650$ yuan to purchase a total of $40$ units of these two models of electric fans, find the maximum profit obtained after all units are sold.

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