
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
Consider a tower made of seven cubes with volumes $1, 27, 64, 125, 216, 343, 512$ cubic units stacked from top to bottom in decreasing order of volume. All cubes are fully aligned along their edges, and each cube sits directly on top of another except for the bottom cube. A special casing covers all but two opposite side faces of each cube (excluding the top and bottom cubes), keeping other faces hidden. Calculate the total visible surface area of the tower, including all faces of the top and bottom cubes and the two side faces of the middle cubes.
A) 630
B) 650
C) 660
D) 670
E) 680

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