
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
"In order to expand the scale of food production, the rice production base plans to invest in purchasing two types of agricultural machinery, A and B. It is known that purchasing 2 units of type A and 1 unit of type B requires a total of 3.5 million yuan, and purchasing 1 unit of type A and 3 units of type B requires a total of 3 million yuan.  
$(1)$ Find out how much money is needed to purchase 1 unit of type A and 1 unit of type B.  
$(2)$ If the rice production base plans to purchase a total of 10 units of type A and B, and the investment is not less than 9.8 million yuan but not more than 12 million yuan, and let the number of units of type A be denoted as $m$, what are the possible purchasing plans?  
$(3)$ Under the conditions of $(2)$, which purchasing plan requires the least amount of money, and how much is the minimum amount?

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