
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

There are $n$ coins arranged along the circumference, each showing heads or tails. If two adjacent coins show the same side (both heads or both tails), you are allowed to flip both. How many distinct configurations of the coins are there that cannot be transformed into one another using these operations?

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