
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 length of the hypotenuse of a right triangle is 3.

a) A scatterbrained Scientist calculated the variance of the lengths of the sides of this triangle and found it to be 2. Did he make a mistake in his calculations?

b) What is the minimum standard deviation of the sides of such a right triangle? What are the lengths of the legs in this case?

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