
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 clothing factory produces a type of clothing, with each piece costing 40 yuan to make and having a factory price set at 60 yuan. To encourage retailers to order, the factory decides that for orders exceeding 100 pieces, the price per piece will decrease by 0.02 yuan for each additional piece ordered. Market research indicates that retailers will not order more than 600 pieces at a time.  
(1) Let the order quantity be $x$ pieces, and the actual factory price per piece be $p$ yuan. Write the expression for the function $p=f(x)$.  
(2) How many pieces should a retailer order to maximize the factory's profit, and what is the maximum profit?

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