
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 endpoints of a diameter of a circle are labeled with the number 1. Divide each resulting semicircle, and write the sum of the numbers at its endpoints at the division points (Step 1). Then, divide the 4 resulting arcs, and write the sum of the numbers at their endpoints at the new division points (Step 2). Continue this process. After a certain number of steps, find the sum of all the numbers written.

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