
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
Some of the 20 metal cubes, identical in size and appearance, are aluminum, while the rest are duralumin (heavier). How can you determine the number of duralumin cubes using 11 weighings on a balance scale with two pans, without using any weights?

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