
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
Zeros and ones are arranged in a circle (both are present). Each number, for which both neighbors are the same, is replaced with a zero, and all other numbers are replaced with ones. This operation is performed multiple times.
a) Can all numbers become zeros if there are 13 of them?
b) Can all numbers become ones if there are 14 of them?

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