
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
Standa assembled 7 identical structures, each made of 8 identical gray cubes with an edge length of $1 \mathrm{~cm}$ as shown in the picture.

Then, he immersed them all in white paint and subsequently disassembled each structure back into the original 8 parts, which now had some faces gray and others white. He also added 8 new cubes that were identical to the others but entirely white. From all the cubes, he constructed one large cube and tried to maximize the gray surface area of the resulting large cube. How many $\mathrm{cm}^{2}$ of the surface will definitely be white?

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