
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 club in a foreign language school has 7 students, among whom 2 students only speak French, 2 students only speak English, and 3 students speak both French and English. Now, 3 students are selected to visit a school in France for an exchange program. Find:<br/>
$(1)$ The probability that exactly 2 of the selected 3 students can speak French;<br/>
$(2)$ The distribution of the number $X$ of students among the selected 3 who can speak both French and English.

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