
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 $\mathbf{a} = \begin{pmatrix} -1 \\ 6 \\ 3 \end{pmatrix},$ $\mathbf{b} = \begin{pmatrix} 3 \\ e \\ 2 \end{pmatrix},$ and $\mathbf{c} = \begin{pmatrix} -4 \\ -1 \\ 5 \end{pmatrix}.$ Compute
\[(\mathbf{a} - \mathbf{b}) \cdot [(\mathbf{b} - \mathbf{c}) \times (\mathbf{c} - \mathbf{a})].\]

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