
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
A sculpture is composed of six cubes with volumes $1$, $27$, $64$, $125$, $216$, and $343$ cubic units, which are placed on one another in descending order of volume. However, due to artistic design, each succeeding cube is rotated so only four of its faces are visible (one face is completely on top of the cube below it, and another is partially hidden by design). Find the total visible surface area of the sculpture in square units.

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