
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
To revitalize the countryside, industries must be revitalized. In many places in Henan Province, relying on ecological advantages and technological support, a significant effort has been made to develop the industry of Morel mushrooms, exploring a new path for the local residents to become prosperous. The village chief of a village in Henan Province led the villagers to revitalize the rural industry by cultivating Morel mushrooms in greenhouses. It is understood that the nutritional value of artificially cultivated Morel mushrooms is equivalent to that of wild Morel mushrooms. A certain retail wholesaler made two purchases at the same unit price in the village for fresh and dried Morel mushrooms as shown in the table below:

|              | Fresh Morel Mushrooms (kg) | Dried Morel Mushrooms (kg) | Total Value (RMB) |
|--------------|-----------------------------|----------------------------|-------------------|
| First Purchase  | 1000                        | 300                        | 152000            |
| Second Purchase | 800                         | 500                        | 184000            |

$(1)$ Find the unit purchase price of fresh and dried Morel mushrooms;  
$(2)$ Due to the good condition of the products, the wholesaler made a third purchase of a total of 1500 kg of both types of Morel mushrooms at the same unit price. According to market demand, the quantity of dried Morel mushrooms purchased must not exceed one-third of the quantity of fresh Morel mushrooms. The retail price of fresh Morel mushrooms in the market is 100 RMB/kg, and the retail price of dried Morel mushrooms is 280 RMB/kg. How should the wholesaler design the purchase plan to maximize profit, and what is the maximum profit?

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