
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 $\mathbf{a}, \mathbf{b}, \mathbf{c}$ be vectors such that $\mathbf{a} + 2\mathbf{b} + \mathbf{c} = \mathbf{0}$. Determine a scalar $m$ such that the equation
\[m (\mathbf{c} \times \mathbf{b}) + \mathbf{a} \times \mathbf{b} + \mathbf{a} \times \mathbf{c} = \mathbf{0}\]
holds.

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