
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, whose volumes are $1$, $27$, $125$, $64$, $343$, $216$, $512$, and $729$ cubic units, are stacked in a vertical tower where the volumes of the cubes decrease from bottom to top. The largest cube at the bottom, every cube exactly covers the one immediately on top and partially overlaps with the second cube on top by one cubic unit except for the top two. Calculate the total surface area of the tower in square units.

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