
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
All students in the second year of a certain school participated in a physical fitness test. It is known that the test score has a maximum of 100 points. The test score is defined as "excellent" if it falls within the interval $[85,100]$, "good" if it falls within $[75,85)$, "passing" if it falls within $[60,75)$, and "failing" if it falls within $[0,60)$. Now, six students are randomly selected from this grade, and their test scores are as follows:

| Student Number | 1   | 2   | 3   | 4   | 5   | 6   |
|----------------|-----|-----|-----|-----|-----|-----|
| Test Score     | 60  | 85  | 80  | 78  | 90  | 91  |

$(Ⅰ)$ If there are 600 students in the second year, estimate the number of "excellent" students: ______;

$(Ⅱ)$ If three students are randomly selected from these six students, let $X$ be the number of "good" students among the three selected. Find the distribution of $X$;

$(Ⅲ)$ Find the mean of $X$ from part $(Ⅱ)$.

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