
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
"Achieving solid results in poverty alleviation and expanding the education track of rural revitalization," a farmer entrepreneur plans to purchase two types of dictionaries, A and B, for Chongli Middle School. It is known that purchasing 1 copy of type A dictionary and 2 copies of type B dictionary costs a total of $170, and purchasing 2 copies of type A dictionary and 3 copies of type B dictionary costs a total of $290.  
$(1)$ Find the price of each type of dictionary.  
$(2)$ The entrepreneur plans to purchase a total of 300 copies of type A and type B dictionaries, with a total cost not exceeding $16000. How many copies of type A dictionary can the entrepreneur purchase at most?

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