
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 created by solid lines in the diagram is composed of 4 congruent squares arranged to form an L-shape. An additional congruent square can be attached to an edge at one of the nine positions indicated on the extended part of the L-shape. Determine how many of the nine resulting polygons can be folded to form a cube with one face missing.
A) 2
B) 3
C) 4
D) 5
E) 6

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