
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
In a math competition study group of a class, there are 9 students. If 3 students are selected from these 9 students, the probability that at least 1 of the selected 3 students is a girl is $\frac{16}{21}$.  
$(1)$ How many male and female students are there in the group?  
$(2)$ If the 9 students stand in a row, and it is required that the male students must stand together in pairs (no 3 male students stand together), how many ways are there to arrange the students? (Answer using numbers)

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