
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 numbers $1, 2, 3, 4, 5$ are placed in a circle. We refer to a placement method as a "Central Ring" placement method if no number $n$ in the range $1$ to $15$ can be formed by adding some adjacent numbers on the circle. If two placement methods can be converted into each other by rotation or reflection, we consider them the same. How many distinct "Central Ring" placement methods are there in total?

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