
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 with dimensions \(3 \times 3 \times 3\) is made of smaller \(1 \times 1 \times 1\) cubes. What is the maximum number of these smaller cubes that can be removed while maintaining a structure with the following two properties:

- From each face of the original cube, the structure looks like a \(3 \times 3\) square (looking perpendicularly to the face, there are no gaps and all 9 cubes are visible);
- It is possible to move from any cube to any other cube through shared faces of the remaining cubes.

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