
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
Suppose \( n \) is a given integer greater than 2. There are \( n \) indistinguishable bags, and the \( k \)-th bag contains \( k \) red balls and \( n-k \) white balls \((k=1,2, \cdots, n)\). From each bag, three balls are drawn consecutively without replacement, and the third ball drawn from each bag is placed into a new bag. What is the expected number of white balls in the new bag?

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