
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 chicken farm plans to purchase a total of 2000 chicks of type A and type B for breeding. It is known that each chick of type A costs 2 yuan, and each chick of type B costs 3 yuan.
(1) If purchasing these chicks costs a total of 4500 yuan, how many chicks of type A and type B were purchased respectively?
(2) If the money spent on purchasing these chicks does not exceed 4700 yuan, what is the minimum number of type A chicks that should be purchased?
(3) According to related data, the survival rates of type A and type B chicks are 94% and 99% respectively. If the survival rate of these chicks needs to be no less than 96% and the total cost is to be minimized, how many chicks of type A and type B should be purchased respectively? What is the minimum total cost?

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