
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
Eight cubes, with volumes of $1$, $8$, $27$, $64$, $125$, $216$, $343$, and $512$ cubic units, are stacked vertically to form a tower in which the volumes of the cubes alternate in rotation by 90 degrees about the vertical axis starting from the second cube. Each cube's bottom face lies completely on top of the cube below it, starting from the largest to the smallest. Calculate the total visible surface area of the tower (including the bottom face of the bottom cube).

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