
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 certain school conducted physical fitness tests on the freshmen to understand their physical health conditions. Now, $20$ students are randomly selected from both male and female students as samples. Their test data is organized in the table below. It is defined that data $\geqslant 60$ indicates a qualified physical health condition.

| Level   | Data Range   | Number of Male Students | Number of Female Students |
|---------|--------------|-------------------------|---------------------------|
| Excellent | $[90,100]$ | $4$                     | $6$                       |
| Good      | $[80,90)$   | $6$                     | $6$                       |
| Pass      | $[60,80)$   | $7$                     | $6$                       |
| Fail      | Below $60$  | $3$                     | $2$                       |

$(Ⅰ)$ Estimate the probability that the physical health level of the freshmen in this school is qualified.  
$(Ⅱ)$ From the students in the sample with an excellent level, $3$ students are randomly selected for retesting. Let the number of female students selected be $X$. Find the distribution table and the expected value of $X$.  
$(Ⅲ)$ Randomly select $2$ male students and $1$ female student from all male and female students in the school, respectively. Estimate the probability that exactly $2$ of these $3$ students have an excellent health level.

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