
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
From a group of $4$ boys and $2$ girls, $2$ people are randomly selected to participate in a speech contest.

$(1)$ Find the probability that both selected people are boys;

$(2)$ Find the probability that exactly one of the selected people is a girl;

$(3)$ Find the probability that at least one of the selected people is a girl.

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