
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 certain type of product with a maximum daily production capacity of 40 units. The ratio of quality products (P) to the total daily production (x, where x is a natural number) is given by the formula P = (4200 - x^2) / 4500. Each quality product generates a profit of 4000 yuan, while each defective product results in a loss of 2000 yuan. (Note: The quality product ratio is calculated as the number of quality products divided by the total number of products, expressed as a percentage.)
(I) Express the daily profit (y, in yuan) as a function of the daily production (x, in units);
(II) Determine the daily production quantity that maximizes the daily profit and calculate the maximum daily profit.

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