
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 school plans to purchase two types of dictionaries, A and B, for teachers. It is known that purchasing 1 copy of dictionary A and 2 copies of dictionary B costs a total of 170 yuan, and purchasing 2 copies of dictionary A and 3 copies of dictionary B costs a total of 290 yuan. <br/> (1) Find the price of each copy of dictionary A and each copy of dictionary B. <br/> (2) The school plans to purchase a total of 30 copies of dictionary A and dictionary B, with a total cost not exceeding 1600 yuan. How many copies of dictionary A can the school purchase at most?

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