
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
Find the sample mean and sample variance using the product method for the given sample distribution with a size of \(n = 100\):

| \( x_{i} \) | 2 | 3 | 7 | 9 | 11 | 12.5 | 16 | 18 | 23 | 25 | 26 |
| ---: | ---: | ---: | ---: | ---: | ---: | :---: | ---: | ---: | ---: | ---: | ---: |
| \( n_{i} \) | 3 | 5 | 10 | 6 | 10 | 4 | 12 | 13 | 8 | 20 | 9 |

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