
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
Given an integer \( n \) greater than 2, there are \( n \) indistinguishable bags. The \( k \)-th bag (where \( 1 \leq k \leq n \)) 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. What is the probability that the third ball drawn is a white ball?

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