
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) How many small cubes form the skeleton of a $6 \times 6 \times 6$ cube?

(b) Given a $7 \times 7 \times 7$ cube made up of $1 \times 1 \times 1$ cubes, how many small cubes need to be removed to obtain the skeleton of the $7 \times 7 \times 7$ cube?

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