
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 measurements of all the edges of a cuboid are whole numbers. The sum of the cuboid's volume, half of its surface area, and the lengths of the edges meeting at one vertex totals 2000. What are the lengths of the edges of the cuboid?

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