
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
From a bag containing \(n-1\) white balls and \(n-1\) black balls, remove all \(2(n-1)\) balls one by one such that after each draw, the number of black balls remaining in the bag is not fewer than the number of white balls remaining in the bag. Assuming balls of the same color are indistinguishable, find the number of possible ways to remove the balls.

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