
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
Four cubes, whose volumes are $1$, $27$, $125$, and $343$ cubic units, are stacked in an alternating manner to form a tower, with the smallest and largest cubes touching the ground. Find the total surface area of the tower, including the bottom.

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