
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
Given vectors $\mathbf{a} = \begin{pmatrix} -3 \\ 5 \\ 2 \end{pmatrix}$, $\mathbf{b} = \begin{pmatrix} 6 \\ -1 \\ 3 \end{pmatrix}$, and $\mathbf{c} = \begin{pmatrix} 1 \\ 2 \\ -4 \end{pmatrix}$, find $\mathbf{a} - 2 \mathbf{b} + \mathbf{c}$.

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