
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
Ten balls are arranged around a circle. Chris chooses three adjacent balls at random and rotates them (i.e., if he chooses balls \(a, b, c\), they become \(b, c, a\)). Silva then chooses another set of three adjacent balls and performs a similar rotation, with her choice and direction of rotation being independent of Chris's. What is the expected number of balls that occupy their original positions after these two successive rotations?
A) 4.5
B) 4.7
C) 4.9
D) 5.1
E) 5.3

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