
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 $3 \times 3 \times 3$ cube is made out of $1 \times 1 \times 1$ smaller cubes. What is the maximum number of smaller cubes that can be removed while ensuring that the remaining structure satisfies the following two properties:

- Looking at any face of the original cube, the structure appears as a $3 \times 3$ square (there are no gaps, and all 9 cubes on each face are visible when looking perpendicularly at that face);
- It is possible to travel from any cube to any other cube within the structure by moving through the shared faces of adjacent cubes.

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