
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 cube with a volume of 1 cubic foot is modified by making three cuts, all parallel to the base. The first cut is $\frac{1}{3}$ foot from the top, the second is $\frac{1}{4}$ foot below the first, and the third is $\frac{1}{6}$ foot below the second. Label the pieces from top to bottom as A, B, C, and D respectively. These pieces are then stacked on top of each other in the order D, C, B, A. Calculate the total surface area of this new solid.

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