
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
When a craft store sells a certain craft at the marked price, it makes a profit of 45 yuan per item. Selling 8 pieces of the craft at 85% of the marked price and selling 12 pieces of the craft at 35 yuan less than the marked price results in equal profit.  
(1) (4 points) What are the cost price and the marked price per piece of the craft?  
(2) (4 points) If each piece of craft is purchased at the cost price found in (1) and sold at the marked price, the craft store can sell 100 pieces of the craft per day. If the price of each piece of craft is reduced by 1 yuan, then 4 more pieces of the craft can be sold each day. How much should the price of each piece of craft be reduced to maximize the daily profit? What is the maximum profit per day?

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