
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 Jiangjin electrical appliance supermarket sells two models of electric fans, $A$ and $B$, with purchase prices of $140$ yuan and $100$ yuan per unit, respectively. The table below shows the sales situation in the past two weeks:

| Sales Period | Quantity of Model $A$ | Quantity of Model $B$ | Sales Revenue $/$ yuan |
|--------------|-----------------------|-----------------------|------------------------|
| Week 1       | 4                     | 3                     | 1250                   |
| Week 2       | 5                     | 5                     | 1750                   |

(Profit = Sales Revenue - Purchase Cost)

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

(2) If the supermarket is prepared to purchase a total of 50 units of these two models of electric fans with no more than 6500 yuan, find the maximum number of units of model $A$ that can be purchased.

(3) Under the condition in (2), can the supermarket achieve a profit goal exceeding 2850 yuan after selling these 50 units of electric fans? If yes, provide the corresponding purchasing plan; if not, explain the reason.

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