
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 certain company's cost for a type of children's toy is 40 yuan, and the factory price is 60 yuan. After market research, adjustments were made. If a distributor orders more than 100 units at a time, for every additional unit ordered, the factory price per toy decreases by 0.02 yuan, but it cannot be lower than 50 yuan.
(1) When the order quantity is how much, the actual factory price per toy is exactly 50 yuan?
(2) If the order quantity is x units, and the actual factory price per toy is exactly w yuan, write the expression for the function $w=f(x)$; and calculate the profit the company makes when a distributor orders 500 toys at one time?

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