
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
Let $(X, Y)$ be a Gaussian system where $Y$ is a random variable in $\mathbb{R}$ and $X$ is a random vector in $\mathbb{R}^{d}$. Determine the structure of the conditional expectations $\mathrm{E}\left(Y^{n} \mid X=x\right)$ for $n \geq 1$.

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