
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 one-cubic-foot cube is sliced into three pieces by two cuts parallel to the top face of the cube. The first cut is $\frac{1}{4}$ foot from the top, and the second cut is $\frac{1}{6}$ foot below the first cut. Find the total surface area of the new solid formed by rearranging and gluing together the three pieces side by side in the same order.

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