
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 middle school plans to purchase two types of school supplies, type A and type B. It is known that the cost of one unit of type A plus the cost of one unit of type B is $40.00. The number of units of type A that can be purchased with $90.00 is the same as the number of units of type B that can be purchased with $150.00.  
$(1)$ Find the cost of one unit of type A and one unit of type B.  
$(2)$ The school plans to purchase a total of 100 units of type A and type B. The total cost of this purchase should not exceed $2000.00. Find the minimum number of units of type A that should be purchased.

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