
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
There are 5 balls in a pocket, all of the same material and size, numbered 1, 2, 3, 4, 5. Players A and B play a game where A draws a ball first, records the number, and then B draws a ball. If the sum of the two numbers is even, A wins; otherwise, B wins.
(I) Calculate the probability that the sum of the numbers is 6.
(II) Is this game rule fair? Explain your answer.
(III) If A does not return the drawn ball, who has the advantage?

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