
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
To further stimulate students' enthusiasm for learning, a certain class has established two interest groups for mathematics and English. The number of students in each group is shown in the table below:

| Group Gender | Mathematics | English |
|--------------|-------------|---------|
| Male         | 5           | 1       |
| Female       | 3           | 3       |

Now, using a stratified sampling method (simple random sampling within each stratum), $3$ students are selected from both groups for testing.

(Ⅰ) Find the probability of selecting at least $1$ female student from the mathematics group.

(Ⅱ) Let $\xi$ be the number of male students selected out of the $3$ students. Find the probability distribution and the expected value of the random variable $\xi$.

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