
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 70th anniversary of the People's Republic of China, a school held a calligraphy and painting competition and prepared to purchase two types of stationery, A and B, to reward outstanding teachers and students in the event. It is known that purchasing 2 items of type A and 1 item of type B costs a total of 35 yuan; purchasing 1 item of type A and 3 items of type B costs a total of 30 yuan.

1. Find out how much it costs to purchase one item of type A and one item of type B each.
2. If the school plans to purchase a total of 120 items of these two types of stationery, with an investment of no less than 955 yuan and no more than 1000 yuan, and assuming x items of type A are purchased, how many different purchasing plans are there?
3. Assuming the school invests W yuan, under the conditions of (2), which purchasing plan requires the least amount of money? How much is the minimum amount of money needed?

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