
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 \(\xi\) be a Gaussian vector in \(\mathbb{R}^{d}\) with a unit covariance matrix. Let the matrix \(B=\left(b_{ij}\right)_{i, j=1}^{d}\) be symmetric and positive definite (\(B>0\)), i.e., such that \(z^{\top} B z > 0\) for all non-zero vectors \(z \in \mathbb{R}^{d}\). For which \(d \geq 1\) does \(\mathrm{E}\left(\xi^{\top} B \xi\right)^{-1}\) exist?

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