
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
A factory produces rectangular doors with a length of 2 meters and a width of 1 meter. The length is measured by a worker named Ivanov, and the width, independently from Ivanov, is measured by a worker named Petrov. Both workers have a zero mean error, but Ivanov has a standard measurement error (standard deviation of length) of 3 mm, and Petrov has a standard measurement error of 2 mm.

a) Find the expected value of the 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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