
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 frequency distribution table of the comprehensive ability test scores (in percentage) of students in a certain class is given below. It is known that there are 21 students in the score range $\left[80,90\right)$.

| Score Range | $\left[65,70\right)$ | $\left[70,75\right)$ | $\left[75,80\right)$ | $\left[80,85\right)$ | $\left[85,90\right)$ | $\left[90,95\right)$ | $\left[95,100\right]$ |
|-------------|----------------------|----------------------|----------------------|----------------------|----------------------|----------------------|----------------------|
| Frequency   | $0.1$                | $0.15$               | $0.2$                | $0.2$                | $0.15$               | $0.1$                | $*$                  |

1. Find the number of students in the score range $\left[95,100\right]$.
2. Now, it is desired to select 2 students from the score range $\left[95,100\right]$ to participate in a physics interest group. If the probability of having at least one male student among the selected 2 students is $\frac{3}{5}$, find the number of male students in the score range $\left[95,100\right]$.
3. If there are 4 female students in the score range $\left[65,70\right)$, and it is desired to select 3 students to participate in an enrichment group from this score range, let $\xi$ be the number of male students selected for this group. Find the distribution table and the expected value $E\xi$ of $\xi$.

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