
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
At a factory, metal discs with a diameter of 1 m are cut. It is known that a disc with a diameter of exactly 1 m weighs exactly 100 kg. During manufacturing, a measurement error occurs, and hence the standard deviation of the radius is 10 mm. Engineer Sidorov believes that a stack of 100 discs will weigh on average 10000 kg. By how much is Engineer Sidorov mistaken?

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