
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 measures \(10 \mathrm{~cm} \times 10 \mathrm{~cm} \times 10 \mathrm{~cm}\). Three cuts are made parallel to the faces of the cube as shown, creating eight separate solids which are then separated. Calculate the increase in the total surface area.

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