
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 $4$-inch edges is constructed from $64$ smaller cubes, each with $1$-inch edges. Out of these smaller cubes, $56$ are colored red and $8$ are colored white. If the $4$-inch cube must be constructed to have at least one white cube showing on each face and still maintain the smallest possible total white surface area, calculate the fraction of the surface area that is white.

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