
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
10 white and 20 black chips are arranged in a circle. It is allowed to swap any two chips that have exactly three chips between them. Two arrangements of chips (in these 30 positions) are called equivalent if one can be transformed into the other by several such swaps. How many non-equivalent arrangements are there?

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