
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
To place $k$ indistinguishable red balls and $k$ indistinguishable white balls into $n$ different boxes, with each box containing only one color of ball, how many different ways are there to distribute the balls? If a red ball is placed, only one can be placed in a single box, and if a white ball is placed, an unlimited number can be placed in any single box. $(1 \leqslant k \leqslant n-1)$

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