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

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