
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 probability density function of a random variable \(X\) is given by

$$
p(x) = a x^{2} e^{-k x} \quad (k > 0, \quad 0 \leq x < +\infty).
$$

Find the value of the coefficient \(a\). Find the cumulative distribution function \(F(x)\) of the random variable \(X\).

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