
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 checkered paper square of size \( 8 \times 8 \) was folded several times along the lines of the grid to form a small \( 1 \times 1 \) square. This small square was then cut along a segment connecting the midpoints of two opposite sides of the square. Into how many parts could the original square break apart by this cut?

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