
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 interest group of a certain class, there are 3 boys and 3 girls. Now, 2 students are randomly selected to participate in the school math competition. Calculate:  
(1) The probability that exactly one of the participants is a boy;  
(2) The probability that at least one of the participants is a boy;  
(3) The probability that at most one of the participants is a boy.

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