
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 tourist city was surveyed, and it was found that the number of tourists per day $f(t)$ (in ten thousand people) and the time $t$ (in days) within the past month (calculated as $30$ days) approximately satisfy the function relationship $f(t)=4+ \frac {1}{t}$. The average consumption per person $g(t)$ (in yuan) and the time $t$ (in days) approximately satisfy the function relationship $g(t)=115-|t-15|$.

(I) Find the function relationship of the daily tourism income $w(t)$ (in ten thousand yuan) and time $t(1\leqslant t\leqslant 30,t\in N)$ of this city;

(II) Find the minimum value of the daily tourism income of this city (in ten thousand yuan).

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