
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
Let $n$ be a given integer greater than 2. There are $n$ indistinguishable bags, and the $k$-th bag $(k= 1,2, \cdots, n)$ contains $k$ red balls and $n-k$ white balls. After mixing these bags, one bag is chosen at random, and three balls are drawn consecutively without replacement. Find the probability that the third ball drawn is white.

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