
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
The polygon enclosed by solid lines consists of 5 congruent squares joined edge-to-edge in a cross shape. One more congruent square is attached to an edge at one of the twelve positions indicated. Determine the number of the resulting polygons that can be folded to form a cube.

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