
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) The Absent-minded Scholar calculated the variance of the lengths of the sides of this triangle and found that it equals 2. Did he make an error in his calculations?

b) What is the minimum possible standard deviation of the sides of such a right triangle? What are the corresponding lengths of the legs?

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