
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
A cube with an edge length of $12 \text{ cm}$ is inscribed in the diagram. An ant sitting at vertex $A$ can only walk along the edges of the cube, without repeating any edge. What is the greatest distance that the ant can travel before it cannot continue?

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