
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
On June 6, 2023, which is the 28th National "Eye Care Day" in China, a city conducted a survey to understand the vision of high school seniors in the city. They randomly selected 200 students' physical examination forms and obtained the statistical data shown in the table below.

| Vision Range | $[4.0,4.2)$ | $[4.2,4.4)$ | $[4.4,4.6)$ | $[4.6,4.8)$ | $[4.8,5.0)$ | $[5.0,5.2)$ |
|--------------|-------------|-------------|-------------|-------------|-------------|-------------|
| Number of Students | 20 | 30 | 70 | 35 | 30 | 15 |

$(1)$ Estimate the average and median of the vision of high school seniors in the city (represent each group of data by the midpoint of the interval, results accurate to $0.1$);  
$(2)$ Define the probability as the proportion. Three students are randomly selected from students in the city with vision not less than $4.8$. Let $X$ be the number of these 3 students whose vision is not less than $5.0$. Find the probability distribution and the expected value of $X$.

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