
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
Green waters and green mountains are all golden mountains and silver mountains. On March 12th, all the students of Class 8 in a certain school, under the leadership of Teacher Deng, planted wishing trees and money trees together. It is known that buying 1 wishing tree and 2 money trees costs 42 yuan, and buying 2 wishing trees and 1 money tree costs 48 yuan.  
$(1)$ Can you calculate the price of each wishing tree and money tree?  
$(2)$ Teacher Deng instructed: the whole class should plant a total of 20 wishing trees and money trees, with the number of wishing trees not less than the number of money trees. However, due to the tight class fund, it is also required that the total cost of the two types of trees does not exceed 312 yuan. Smart students, do you know which planting schemes are available?

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