
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
We place labeled points on a circle as follows. At step 1, take two points at opposite ends of a diameter and label them both 1. At step \(n > 1\), place a point at the midpoint of each arc created at step \(n-1\) and label it with the sum of the labels at the two adjacent points. What is the total sum of the labels after step \(n\)? For example, after step 4 we have: 1, 4, 3, 5, 2, 5, 3, 4, 1, 4, 3, 5, 2, 5, 3, 4.

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