
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 market survey shows that the price $f(x)$ (in yuan) and the sales volume $g(x)$ (in units) of a certain product in the past $20$ days are both functions of time $x$ (in days), and the price satisfies $f(x)=20-\frac{1}{2}|x-10|$, and the sales volume satisfies $g(x)=80-2x$, where $0\leqslant x\leqslant 20$, $x\in N$.
(1) Write the function expression of the daily sales $y$ (in yuan) of the product with time $x$ (in days).
(2) Find the minimum value of the daily sales of the product.

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