
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]


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A math interest group in a class has three male students, denoted as \(a_{1}\), \(a_{2}\), \(a_{3}\), and two female students, denoted as \(b_{1}\), \(b_{2}\). Now, two students are randomly selected to participate in the school math competition.

(1) Write out the sample space for this selection method;

(2) Calculate the probability that exactly one male student is among the participants;

(3) Calculate the probability that there is at least one male student among the participants.

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