
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 math interest group consists of 2 boys, labeled as a and b, and 3 girls, labeled as c, d, and e. Now, 2 students are to be selected from the group to participate in a school math competition.  
(1) List all the basic events and calculate their number;  
(2) Calculate the probability that exactly one boy is among the students participating in the competition;  
(3) Calculate the probability that at least one boy is among the students participating in the competition.

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