
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 cubic block with dimensions  $n$  by  $n$  by  $n$  is made up of a collection of  $1$  by  $1$  by  $1$  unit cubes. What is the smallest value of  $n$  so that if the outer two layers of unit cubes are removed from the block, more than half the original unit cubes will still remain?

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