
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 middle school plans to purchase a batch of banyan trees and camphor trees to green the campus. According to market research, the unit price of banyan trees is $20$ yuan less than that of camphor trees. It costs a total of $340$ yuan to purchase $3$ banyan trees and $2$ camphor trees.<br/>$(1)$ Please find out the unit price of banyan trees and camphor trees respectively.<br/>$(2)$ Based on the actual situation of the school, they need to purchase a total of $150$ seedlings of the two types of trees, with a total cost not exceeding $10840$ yuan. The number of camphor trees purchased should be at least $1.5$ times the number of banyan trees. Please calculate the possible combinations of purchasing banyan trees and camphor trees this time.

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