
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
Zuzka built a square with dimensions $4 \times 4$ using sixteen equally sized cubes. She continued building using the same type of cubes, stacking them such that each pair of adjacent cubes shared an entire face. The final structure looked from two different sides like in the following picture.

Determine the maximum and minimum number of cubes Zuzka could have used for her construction.

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