
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
To celebrate the National Day, our school is holding a calligraphy and painting competition and is preparing to purchase two types of stationery, A and B, to reward outstanding teachers and students during the event. It is known that purchasing 2 units of type A stationery and 1 unit of type B stationery costs a total of 35 yuan; purchasing 1 unit of type A stationery and 3 units of type B stationery costs a total of 30 yuan.  
$(1)$ Find out how much each unit of type A and type B stationery costs when purchasing one unit of each.  
$(2)$ If the school plans to purchase a total of 120 units of these two types of stationery, with an investment of no less than 975 yuan and no more than 1000 yuan, and let the number of units of type A stationery be x, determine which purchasing schemes are feasible.  
$(3)$ Under the conditions in (2), which purchasing scheme requires the least amount of money? How much is the minimum amount?

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