
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 factory produces a type of product with a raw material cost of 40 yuan per item. If $x$ represents the total number of products produced by the factory, then the cost of electricity and machine maintenance is 0.05x yuan per item. Additionally, the factory's fixed expenditure on worker wages is 12,500 yuan.
(1) Express the cost per product $P(x)$ (in yuan) as a function of the number of products $x$, and find the minimum cost per product;
(2) If the factory produces no more than 3000 items of this product, and all products can be sold, according to market research: the selling price per product $Q(x)$ has the following relationship with the number of products $x$: $Q(x) = 170 - 0.05x$. How many products should be produced to maximize the total profit? (Total profit = Total sales - Total cost)

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