
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 grid lines to form a \(1 \times 1\) square. This small square was then cut along the segment connecting the midpoints of two opposite sides of the square. Into how many parts could the original square split after this cut?

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