
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
Dima cut a cardboard square $8 \times 8$ along the boundaries of the cells into six parts (see picture). It turned out that the square remained sturdy: if you place it on a table and pull any piece in any direction, the entire square moves together with that piece.

Show how to cut such a square along the boundaries of the cells into at least 27 parts, so that the square remains sturdy and each part contains no more than 16 cells.

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