
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
In recent years, a company has been spending approximately 240,000 yuan on electricity annually. To save energy and reduce emissions, the company decided to install a solar power generation device that can be used for 15 years and connected to the company's power grid. The installation cost (in 10,000 yuan) of this device is proportional to the area of the solar panels (in square meters), with a proportionality constant of approximately 0.5. To ensure normal electricity usage, the company will adopt a complementary power supply mode using both solar and grid electricity after the installation. Assume that under this mode, the annual electricity cost C (in 10,000 yuan) of the company after the installation and the area x (in square meters) of the installed solar panels have the functional relationship C(x) = k / (20x + 100) (x ≥ 0, k is a constant). Let F represent the sum of the cost of installing the solar power generation device and the total electricity cost that the company will consume in 15 years.
(1) Explain the practical meaning of C(0) and establish the functional relationship of F with respect to x;
(2) When x is how many square meters, F takes the minimum value? What is the minimum value in 10,000 yuan?

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