
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 larger cube with 4-inch edges is to be constructed from 64 smaller cubes with 1-inch edges, 52 of which are colored red and 12 are colored white. If the 4-inch cube is constructed to have the smallest possible white surface area showing, calculate the fraction of the surface area that is white.

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