
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]


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A random variable \( X \) is defined by the probability density function \( f(x) = \frac{x^n e^{-x}}{n!} \) for \( x \geq 0 \); \( f(x) = 0 \) for \( x < 0 \). Find: a) the expected value; b) the variance of \( X \).

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