
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
Nine balls are arranged around a circle. Chris always chooses to swap the first and second balls, and then Silva swaps the fourth and fifth balls. What is the expected number of balls that remain in their original positions after these two specific transpositions?

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