
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 a privately-owned company in Wenzhou manufacturing a product, it is known from past data that the fixed daily cost of producing the product is 14,000 RMB. The variable cost increases by 210 RMB for each additional unit produced. The relationship between the daily sales volume $f(x)$ and the production quantity $x$ is given as follows:
$$
f(x)= 
\begin{cases}
\frac{1}{625} x^2 & \quad \text{for } 0 \leq x \leq 400, \\
256 & \quad \text{for } x > 400,
\end{cases}
$$
The relationship between the selling price per unit $g(x)$ and the production quantity $x$ is given as follows:
$$
g(x)= 
\begin{cases}
- \frac{5}{8} x + 750 & \quad \text{for } 0 \leq x \leq 400,\\
500 & \quad \text{for } x > 400.
\end{cases}
$$
(I) Write down the relationship equation between the company's daily sales profit $Q(x)$ and the production quantity $x$;  
(II) To maximize daily sales profit, how many units should be produced each day, and what is the maximum profit?

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