
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 mobile phone distributor plans to purchase a batch of two models of phones, A and B, at the same time. If they buy 2 units of model A and 1 unit of model B, it will cost $5000. If they buy 3 units of model A and 2 units of model B, it will cost $8000.  
$(1)$ Find the purchase price per unit of model A and model B.  
$(2)$ The store plans to purchase and sell both model A and model B phones, planning to spend no more than $26,000 and no less than $24,000 to purchase a total of 20 phones. How many purchasing plans are there? Please list the purchasing plans.

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