
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 \(\mathbf{d} = \begin{pmatrix} -4 \\ 12 \\ 2 \end{pmatrix},\) \(\mathbf{e} = \begin{pmatrix} 6 \\ 2\pi \\ 1 \end{pmatrix},\) and \(\mathbf{f} = \begin{pmatrix} -1 \\ -1 \\ 9 \end{pmatrix}.\) Compute
\[
2 \cdot (\mathbf{d} - 2\mathbf{e}) \cdot [(\mathbf{e} - \mathbf{f}) \times (\mathbf{f} - \mathbf{d})].
\]

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