
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 $m$ be a scalar such that for any vectors $\mathbf{p}$, $\mathbf{q}$, and $\mathbf{r}$ satisfying $\mathbf{p} + \mathbf{q} + \mathbf{r} = \mathbf{0}$, the equation
\[m (\mathbf{q} \times \mathbf{p}) + 2\mathbf{q} \times \mathbf{r} + 2\mathbf{r} \times \mathbf{p} = \mathbf{0}\] holds. Find the scalar $m$.

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