
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]


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A new model of polymorphic cubes exists, each with a snap on one side and receptacles on the remaining five sides. The cubes can only be connected via these snaps fitting into receptacles. Determine the minimum number of cubes required to build a fully enclosed structure such that all snaps are either inserted into another cube's receptacle or are internally facing and not visible from the outside.

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