
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 large event, five volunteers, including A and B, are randomly assigned to four different positions: _\\(A\\)_, _\\(B\\)_, _\\(C\\)_, and _\\(D\\)_, with each position being served by at least one volunteer.

\\((1)\\) Calculate the probability that both A and B serve at position _\\(A\\)_ simultaneously;

\\((2)\\) Calculate the probability that A and B serve at different positions;

\\((3)\\) Calculate the probability that exactly one out of the five volunteers serves at position _\\(A\\)_.

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