
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 company produces a certain product with an annual fixed cost of 250,000 yuan. In addition, each unit of this product produced incurs an additional cost of 5,000 yuan. Market research indicates that the annual demand for this product is 500 units. When the number of products sold is $t$ units, the revenue from sales is $$(5t- \frac {1}{200}t^{2})$$ thousand yuan.
(1) If the annual production quantity of this product is $x$ units, find the profit function $f(x)$ with respect to the production quantity $x$ for that year.
(2) At what annual production quantity does the company maximize its profit for the year?

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