
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
Ana has an iron material of mass  $20.2$  kg. She asks Bilyana to make  $n$  weights to be used in a classical weighning scale with two plates. Bilyana agrees under the condition that each of the  $n$  weights is at least  $10$  g. Determine the smallest possible value of  $n$  for which Ana would always be able to determine the mass of any material (the mass can be any real number between  $0$  and  $20.2$  kg) with an error of at most  $10$  g.

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