
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
A sample with size $n=10$ is taken from a population:

\[
\begin{array}{lllllllll}
\text{variant} & x_{i} & -2 & 1 & 2 & 3 & 4 & 5 \\
\text{frequency} & n_{i} & 2 & 2 & 2 & 2 & 2 & 1
\end{array}
\]

Estimate with 95% confidence the mathematical expectation $a$ of the normally distributed characteristic of the population using the sample mean through a confidence interval.

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