
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 \(\mathbf{a} = \begin{pmatrix} 8 \\ -3 \\ 1 \end{pmatrix}\) and \(\mathbf{c} = \begin{pmatrix} 2 \\ 1 \\ -3 \end{pmatrix}\). Find the vector \(\mathbf{b}\) such that \(\mathbf{a}, \mathbf{b},\) and \(\mathbf{c}\) are collinear, and \(\mathbf{b}\) bisects the angle between \(\mathbf{a}\) and \(\mathbf{c}\).

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