
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
World Book Day on April 23 is officially known as "World Book and Copyright Day," also known as "World Book Day." The original idea came from the International Publishers Association. The plan was passed from Spain to the United Nations Educational, Scientific and Cultural Organization. On November 15, 1995, April 23 was officially designated as "World Book Day" each year. The purpose of its establishment is to promote more people to read and write, hoping that everyone can respect and thank the literary, cultural, scientific, and intellectual masters who have made great contributions to human civilization, and protect intellectual property. On this day each year, more than 100 countries around the world will hold various celebrations and book promotion activities. On the occasion of World Book Day in 2023, a high school reading association conducted a random survey of 50 senior high school students to study the impact of extracurricular reading time on Chinese language scores. Each student's average daily extracurricular reading time (in minutes) and their Chinese language scores were recorded, and the following statistical table was obtained:

| Reading Time | $(0,20]$ | $(20,40]$ | $(40,60]$ | $(60,80]$ | $(80,100]$ |
|--------------|----------|-----------|-----------|-----------|------------|
| Number of Students | $5$ | $15$ | $20$ | $5$ | $5$ |
| Excellent Chinese Score | $11$ | $1$ | $1$ | $4$ | $4$ |

$(1)$ Estimate the mean and median of the daily extracurricular reading time of senior high school students in this school. (Represent the data in each group by the midpoint value of that group)  
$(2)$ If three students are randomly selected from the students in the $(60,80]$ interval to study their Chinese language scores, find the probability that all three students have excellent Chinese scores.

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