
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
Given a configuration of six congruent squares forming an 'F' shape, where squares are numbered from 1 through 6 beginning from the top left and moving horizontally across two rows. An additional congruent square can be placed adjacent to this structure at one of the ends of the 'F' shape. How many positions are there such that, by folding the modified polygon, one can form a three-dimensional geometric structure with exactly one square forming a top that is open? Assume open top does not require enclosure by another square shape.
A) 1
B) 2
C) 3
D) 4
E) 5

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