
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
Arrange 6 balls in a line, where balls 1, 2, and 3 are black and balls 4, 5, and 6 are white. If you swap balls 2 and 5, the 6 balls become alternately black and white. Now, given 20 balls in a line, where balls 1 to 10 are black and balls 11 to 20 are white, what is the minimum number of swaps needed to arrange these 20 balls alternately in black and white?

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