
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 $\mathbf{u} = \begin{pmatrix} 4 \\ -2 \\ -1 \end{pmatrix},$ $\mathbf{v} = \begin{pmatrix} -2 \\ -3 \\ 6 \end{pmatrix},$ and $\mathbf{w} = \begin{pmatrix} 3 \\ 7 \\ 0 \end{pmatrix}.$ Compute
\[
(\mathbf{u} - \mathbf{v}) \cdot [(\mathbf{v} - \mathbf{w}) \times (\mathbf{w} - \mathbf{u})].
\]

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