
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
Each bag of sugar has a standard weight of $500$ grams. The quality supervision department wants to understand the weight condition of a batch of sugar. They randomly selected $9$ bags and weighed each bag (in grams) as follows:
$490$   $495$   $493$   $498$   $499$   $500$   $503$   $507$   $506$
(I) Calculate the mean and standard deviation of these values;
(II) If two bags are randomly confiscated from the five bags that are lighter than the standard weight, calculate the probability that the weights of these two bags are both below the mean.

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