
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
Given that eight cubes with volumes $1$, $8$, $27$, $64$, $125$, $216$, $343$, $512$ cubic units are stacked vertically to form a tower in which the volumes of the cubes decrease from bottom to top, calculate the total surface area of the new tower in square units.

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