
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 $f(t)$ and sales volume $g(t)$ of a particular product in Oriental Department Store over the past month (calculated based on 30 days) approximately satisfy the functions $f(t)=100(1+ \frac {1}{t})$ and $g(t)= \begin{cases} 100+t & 1\leqslant t < 25,t\in N \\ 150-t & 25\leqslant t\leqslant 30,t\in N \end{cases}$, respectively.
(1) Find the daily sales revenue $W(t)$ of the product in terms of time $t (1\leqslant t\leqslant 30,t\in N)$;
(2) Calculate the maximum and minimum daily sales revenue $W(t)$.

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