
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 setting the factory price at \\(60\\) yuan. To encourage orders from retailers, the factory decides that for orders exceeding \\(100\\) pieces, the factory price per piece will decrease by \\(0.02\\) yuan for each additional piece ordered. Market research indicates that retailers will not order more than \\(500\\) pieces at a time.  
\\((I)\\) Let the order quantity be \\(x\\) pieces, and the actual factory price be \\(P\\) yuan. Write the expression for the function \\(P=f(x)\\);  
\\((II)\\) When a retailer orders \\(450\\) pieces at once, what is the profit for the clothing factory?  
\\((\\)The profit for the factory from selling one piece of clothing \\(=\\) actual factory price \\(-\\) cost\\()

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