
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
Five cubes, whose volumes are $1$, $64$, $27$, $343$, and $125$ cubic units, are arranged in a staggered vertical tower. The bottom cube has a volume of $343$ cubic units, followed by $125$, $27$, $64$, and $1$ at the top. Except for the base of the bottom and the top of the topmost cube, the surfaces visible include: partial top faces of all cubes but the highest and partial side faces depending on the arrangement overlap. Determine the total visible surface area in square units.
A) 370
B) 400
C) 450
D) 500

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