
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
Given a circular chip placed as a centerpiece, calculate the number of identical chips that can be arranged around it, with every chip in the outer layer required to be tangent to exactly two others in its layer and to two centerpieces, forming the most compact arrangement possible.

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