
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 in a circle. Chris and Silva each select two adjacent balls at random in turns and interchange them, followed by Alex selecting two adjacent balls at random and interchanging them. Determine the expected number of balls that are in their original positions after these three successive transpositions.

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