
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 faces of a parallelepiped with dimensions \( a \times b \times c \) are divided into unit squares. Additionally, there are a large number of five-cell strips that can be folded along the boundaries of the unit squares. For which values of \( a \), \( b \), and \( c \) can the three faces of the parallelepiped that share a common vertex be completely covered with these strips without overlaps or gaps, so that the unit squares of the faces align perfectly with those of the strips?

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