
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

Given an $n \times n \times n$ cube consisting of $n^{3}$ unit cubes (henceforth referred to as "cells"), any two cells $A$ and $B$ are said to be "adjacent" if they share a common face, or if there exists a cell $C$ such that both $A$ and $B$ share a common face with $C$. Color each cell of an $n \times n \times n$ cube with one of $r$ colors such that any two adjacent cells have different colors. Find the minimum value of $r$.

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