
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 \(\mathbf{a} = \begin{pmatrix} -4 \\ 9 \\ 2 \end{pmatrix},\) \(\mathbf{b} = \begin{pmatrix} 7 \\ e \\ -1 \end{pmatrix},\) and \(\mathbf{c} = \begin{pmatrix} -1 \\ -1 \\ 8 \end{pmatrix}.\) Compute
\[
(\mathbf{a} - \mathbf{b}) \cdot [(\mathbf{b} - \mathbf{c}) \times (\mathbf{c} - \mathbf{a})].
\]

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