
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 student interest group randomly surveyed the air quality level and the number of people exercising in Jinshan Park in our area for 100 days. The corresponding number of days is summarized in the table below (unit: days),

| Exercise Times ($x$) | Days | Air Quality Level |
|----------------------|------|-------------------|
| $0\leqslant x \lt 200$ | | |
| $200\leqslant x \lt 400$ | | |
| $400\leqslant x \lt 600$ | | |
| $Ⅰ(Excellent)$ | $3$ | $18$ | $28$ |
| $Ⅱ(Good)$ | $5$ | $9$ | $11$ |
| $Ⅲ(Mild Pollution)$ | $5$ | $6$ | $6$ |
| $Ⅳ(Moderate Pollution)$ | $7$ | $2$ | $0$ |

(1) Please estimate the probability of the air quality level being $Ⅰ$ in our area for a day;  
(2) Find the estimated average number of people exercising in Jinshan Park in our area for a day. (Use the mid-value of the data range in the group to represent the data in the same group)

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