
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 distributed according to the exponential law with the probability density function

$$
p(x, \lambda)=\lambda e^{-\lambda x} \quad \text{for} \quad x \geq 0 \quad \text{and} \quad p(x, \lambda)=0 \quad \text{for} \quad x < 0,
$$

where $\lambda$ is an unknown parameter. Given the sample

$$
0.61, 0.71, 1.27, 0.10, 1.49, 1.14, 2.15, 0.06, 0.74, 0.28,
$$

find the confidence interval for $\lambda$ at a confidence level of $p = 0.8$.

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