
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 found that the sales volume and price of a certain small commodity in a supermarket in the past 20 days are both functions of time $t$ (days). The sales volume approximately satisfies $g(t)=80-2t$ (units), and the price approximately satisfies $f(t)=20- \frac{1}{2}|t-10|$ (yuan).
(1) Write the function expression of the daily sales $y$ of this commodity with time $t$ ($0\leqslant t\leqslant 20$);
(2) Find the maximum and minimum values of the daily sales $y$.

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