
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 company has developed 1000 new products that require fine processing before they can be launched on the market. Currently, Factory A and Factory B are processing this batch of products. It is known that Factory A, working alone, would take 10 days more to complete the processing of this batch of products than Factory B working alone. The daily processing capacity of Factory B is 1.25 times that of Factory A. The company needs to pay Factory A a processing fee of 100 yuan per day, and Factory B a processing fee of 125 yuan per day.

(1) How many new products can each factory process per day?
(2) If both factories work together to complete the processing of this batch of products, how much will the total processing fee be?

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