
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 $\mathbf{u},$ $\mathbf{v},$ $\mathbf{w}$ be vectors in $\mathbb{R}^3$, and let $E$ be the determinant of the matrix whose column vectors are $\mathbf{u},$ $\mathbf{v},$ and $\mathbf{w}.$ Find the determinant of the matrix whose column vectors are $\mathbf{u} \times \mathbf{v},$ $\mathbf{v} \times \mathbf{w},$ and $\mathbf{w} \times \mathbf{u}$ and express it in terms of $E$.

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