
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 random variable $\xi$ is normally distributed with parameters $a$ and $\sigma^{2}$. Given a sample $x_{1}, \ldots, x_{n}$ of values of $\xi$ with empirical moments $M_{1}^{*}=\bar{x}=2.3$ and $M_{2}^{*}=\overline{x^{2}}=8.7$. Using these moments, find the parameters $a$ and $\sigma^{2}$.

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