
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 the vectors \(\mathbf{a} = \begin{pmatrix} 4 \\ 2 \\ -3 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} 1 \\ 3 \\ -2 \end{pmatrix}\). We are given that there are scalars \(p,\) \(q,\) and \(r\) such that
\[
\begin{pmatrix} 5 \\ 4 \\ -8 \end{pmatrix} = p \mathbf{a} + q \mathbf{b} + r (\mathbf{a} \times \mathbf{b}).
\]
Determine the value of \(r\).

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