
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 cylindrical container with a height of 1 foot and a base radius of 1 foot is sectioned into four parts by three horizontal cuts. 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 $\frac{1}{6}$ below the second. Calculate the total exposed surface area (excluding any touching surfaces between the sections) of the new arrangement in square feet.

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