
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
Given that the cost C (in ten-thousand yuan) of manufacturing a certain brand car is related to the monthly production x (in units) by the function $C = 100 + 4x$, and the unit price p is related to the production x by the function $p = 25 - \frac{1}{8}x$, assuming all products are sold.
(1) Find the expression for the profit function $f(x)$ and state its domain.
(2) What is the value of the monthly production x that maximizes profit, and what is the maximum profit?

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