
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 garment that costs 40 yuan each to manufacture. The factory sets the wholesale price at 60 yuan per piece. To encourage orders from retailers, the factory decides to offer a discount: for any order exceeding 100 pieces, the wholesale price per garment is reduced by 0.02 yuan for each additional piece ordered. According to market research, retailers will not order more than 500 pieces at a time.
(I) Let the order quantity be $x$ pieces and the actual wholesale price be $P$ yuan per piece. Write the expression for the function $P=f(x)$.
(II) How much profit does the factory make when a retailer orders 450 pieces of the garment? (Profit per garment = actual wholesale price - cost)

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