
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 \(2 \times 2 \times 2 \text{ cm}\) cube has a \(1 \times 1 \times 1 \text{ cm}\) cube removed from it to form the shape shown in the left-hand diagram. One of these shapes is inverted and put together with a second of the shapes on a flat surface, as shown in the right-hand diagram.
What is the surface area of the new shape?

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