
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 school plans to purchase camphor trees and osmanthus trees in two separate purchases to green the campus environment. In the first purchase, they bought 20 camphor tree seedlings and 10 osmanthus tree seedlings for a total of 3000 yuan. In the second purchase, they bought 24 camphor tree seedlings and 8 osmanthus tree seedlings for a total of 2800 yuan. (The unit prices of the two types of seedlings in the two purchases remain the same)<br/>$(1)$ What is the unit price of each type of seedling in yuan?<br/>$(2)$ The school plans to purchase a total of 40 seedlings of the two types in the next purchase, but the total cost should not exceed 3800 yuan, and the number of camphor tree seedlings purchased should not exceed three times the number of osmanthus tree seedlings. What are the possible purchasing schemes?

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