
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
From a solid regular tetrahedron with edge length of one unit, a smaller regular tetrahedron with an edge length of $\frac{1}{n}$ is cut off from each of its vertices, where $n$ is an integer greater than 1. For what value of $n$ will the ratio of the surface area to the volume of the remaining solid be minimized?

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