
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 response to the call for rural revitalization, Xiao Jiao, a college graduate who has successfully started a business in another place, resolutely returned to her hometown to become a new farmer and established a fruit and vegetable ecological planting base. Recently, in order to fertilize the vegetables in the base, she is preparing to purchase two types of organic fertilizers, A and B. It is known that the price per ton of organic fertilizer A is $100 more than the price per ton of organic fertilizer B, and the total cost of purchasing 2 tons of organic fertilizer A and 1 ton of organic fertilizer B is $1700.  
$(1)$ How much is the price per ton of organic fertilizer A and B respectively?  
$(2)$ If Xiao Jiao is preparing to purchase a total of 10 tons of organic fertilizers A and B, and the total cost cannot exceed $5600, how many tons of organic fertilizer A can Xiao Jiao purchase at most?

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