
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 \(\mathbf{p} = \begin{pmatrix} -1 \\ 4 \\ 2 \end{pmatrix}, \mathbf{q} = \begin{pmatrix} 3 \\ 5 \\ -1 \end{pmatrix},\) and \(\mathbf{r} = \begin{pmatrix} 0 \\ 3 \\ 9 \end{pmatrix}.\) Compute
\[
(\mathbf{p} - \mathbf{q}) \cdot [(\mathbf{q} - \mathbf{r}) \times (\mathbf{r} - \mathbf{p})].
\]

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