
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
At the ends of the diameter of a circle, there are units. Each of the resulting semicircles is divided in half, and in its middle, the sum of the numbers at the ends is written (first step). Then, each of the four resulting arcs is divided in half, and in its middle, a number equal to the sum of the numbers at the ends of the arc is written (second step). This operation is performed $n$ times. Find the sum of all the recorded numbers.

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