
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
Alice has a sheet of cardboard measuring 60 by 25 cm. She wants to cut the sheet to assemble a cube, with edges measuring an integer number of centimeters. Allowing cuts but not allowing overlap, what is the cube with the largest volume that she can build?

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