
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
Three friends, Chris, Silva, and Alex, are playing a game with six balls arranged in a circle. Each one of them, in turn, chooses two adjacent balls and swaps their positions. The choice of each person is independent of the others. What is the expected number of balls that occupy their original positions after Chris, Silva, and Alex have each made one swap?
\(\textbf{A})\: 1.0\)
\(\textbf{B})\: 1.5\)
\(\textbf{C})\: 2.0\)
\(\textbf{D})\: 2.5\)
\(\textbf{E})\: 3.0\)

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