
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
Find the initial moments of the random variable \( X \) with the probability density function

\[ 
p(x) = 
\begin{cases} 
0 & \text{if } x \leq 1 \\ 
\frac{5}{x^{6}} & \text{if } x > 1 
\end{cases} 
\]

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