
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
Seven balls are arranged around a circle. Chris, Silva, and Alex each in turn choose two adjacent balls at random and interchange them. Each choice is independent of the others. What is the expected number of balls that occupy their original positions after these three successive transpositions?
A) 2.4
B) 2.5
C) 2.6
D) 2.7
E) 2.8

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