
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
Create a cube \( C_{1} \) with edge length 1. Take the centers of the faces and connect them to form an octahedron \( O_{1} \). Take the centers of the octahedron's faces and connect them to form a new cube \( C_{2} \). Continue this process infinitely. Find the sum of all the surface areas of the cubes and octahedrons.

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