
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 support the 2010 Asian Games in Guangzhou, a class in a school in Guangzhou plans to send 4 volunteers to participate in the Asian Games. After a preliminary selection, 5 boys and 4 girls, a total of 9 students, were identified as candidates. Each candidate has an equal chance of being selected as a volunteer.  
(1) What is the probability that 1 girl and 3 boys are selected?  
(2) Let $P_n$ be the probability that at least $n$ male students are selected. When $P_{n} \geq \frac{3}{4}$, what is the maximum value of $n$?

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