
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
Ten cubes, whose volumes are $1$, $8$, $27$, $64$, $125$, $216$, $343$, $512$, $729$, and $1000$ cubic units, are stacked to form a tower in an alternating pattern where odd indexed cubes (from the bottom) have their faces unable to see downwards while even indexed cubes have one face unable to see upwards, except for the topmost cube. Compute the total surface area of the tower.
A) 1901
B) 1986
C) 2026
D) 2105
E) 2250

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