
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 random variable $\xi$ is normally distributed with unknown mean $a$ and variance $\sigma^{2}$. A sample of values $x_{1}, \ldots, x_{10}$ from this distribution is given. The sample mean is 1.17, and the sample variance is 0.25. Find the confidence intervals for $a$ and $\sigma^{2}$ at confidence levels $p_{a}=0.98$ and $p_{\sigma^{2}}=0.96$.

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