
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
The factory named after sailor Zheleznyak produces 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. Both workers have zero mean measurement 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 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