
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
The field consists of ten circles connected by lines. Black pieces stand in the four upper circles, and gray pieces stand in the four lower circles. Pieces can be moved along the lines to a free circle. How can the black and gray pieces be swapped?

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