
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 parallelepiped $a \times b \times c$ has faces divided into unit cells. There are also a large number of three-cell strips that can be bent at the boundaries of the cells. For which $a, b$, and $c$ can the three faces of the parallelepiped that share a common vertex be completely covered with strips without overlaps and gaps so that the cells of the faces and the strips match?

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