
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
There are 6 international game volunteers, among whom volunteers $A\_1$, $A\_2$ are proficient in French, $B\_1$, $B\_2$ in Russian, and $C\_1$, $C\_2$ in English. One volunteer proficient in each language is to be selected to form a group.

(1) Calculate the probability that $A\_1$ is selected.
(2) Calculate the probability that both $B\_1$ and $C\_1$ are not selected.
(3) If these 6 volunteers take turns to be on duty in pairs every hour, calculate the probability that two French-speaking athletes will encounter exactly $A\_1$, $A\_2$.

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