
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 $n$ white balls and $n$ black balls, draw $2n$ balls one by one, ensuring that the number of black balls remaining in the bag is never less than the number of white balls remaining in the bag at any point during the process. Assuming that balls of the same color are indistinguishable, find the number of all possible ways to draw the balls.

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