
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 out of 20 metal cubes, identical in size and appearance, are made of aluminum, and the rest are made of duralumin (which is heavier). How can you determine the number of duralumin cubes using no more than 11 weighings on a balance scale without weights?

Note. It is assumed that all the cubes could be made of aluminum, but they cannot all be made of duralumin (because if all the cubes turned out to be of the same weight, we wouldn't be able to determine whether they are aluminum or duralumin without this condition).

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