
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
List the circular series $\breve{\Phi}_{2}^{0}, \breve{\Phi}_{3}^{0}, \breve{\Phi}_{4}^{0}, \breve{\Phi}_{5}^{0}, \breve{\Phi}_{6}^{0}, \breve{\Phi}_{7}^{0}$, $\breve{\Phi}_{8}^{0}, \breve{\Phi}_{9}^{0}, \breve{\Phi}_{10}^{0}, \breve{\Phi}_{11}^{0}$ (the symbol $\breve{\Phi}_{m}^{0}$ denotes a circular $m$-arithmetic Fibonacci series without repetitions, containing the pair 0,1).

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