
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 shopping mall plans to purchase two types of goods, A and B. If purchasing 20 pieces of product A and 15 pieces of product B requires 380 yuan, and purchasing 15 pieces of product A and 10 pieces of product B requires 280 yuan,  
(1) What are the purchase prices of products A and B respectively?  
(2) If purchasing a total of 100 pieces of products A and B, with a total cost not exceeding 900 yuan, what is the maximum number of product A pieces that can be purchased?

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