
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
In order to green the barren mountains, a village plans to plant cypress and pine trees on Arbor Day. After investigation, it is found that buying 2 cypress trees and 3 pine trees costs a total of $850, and buying 3 cypress trees and 2 pine trees costs a total of $900.  
$(1)$ Find the unit price of cypress and pine trees.  
$(2)$ For this greening project, 80 cypress and pine trees are needed, with the number of cypress trees being at least twice the number of pine trees. In order to minimize the cost of purchasing trees, how many cypress and pine trees should be purchased? What is the minimum cost?

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