
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 meters and a width of 1 meter. The length is measured by worker Ivanov, and the width, independently of Ivanov, is measured by worker Petrov. The average error for both is zero, 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}
user