
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 \(\mathbf{a} = \begin{pmatrix} 4 \\ -7 \\ 2 \end{pmatrix}\), \(\mathbf{b} = \begin{pmatrix} -2 \\ 3 \\ -1 \end{pmatrix}\), and \(\mathbf{c} = \begin{pmatrix} 5 \\ -1 \\ 8 \end{pmatrix}\). Compute
\[
3(\mathbf{a} + 2\mathbf{b}) \cdot [2(\mathbf{b} + \mathbf{c}) \times (3\mathbf{c} - 2\mathbf{a})].
\]

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