
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 the factory named after sailor Zheleznyak, they manufacture rectangles with a length of 2 m and a width of 1 m. The length is measured by worker Ivanov, while the width, independently from Ivanov, is measured by worker Petrov. Both have an average measurement error of zero, but Ivanov has a standard measuring error (standard deviation of the length) of 3 mm, and Petrov has a standard measuring error of 2 mm.

a) Find the expected area of the resulting rectangle.

b) Find the standard deviation of the area of the resulting rectangle in square centimeters.

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