
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 $\mathbf{a}, \mathbf{b}, \text{ and } \mathbf{c}$ be three mutually orthogonal unit vectors, such that
\[
\mathbf{a} = p (\mathbf{a} \times \mathbf{b}) + q (\mathbf{b} \times \mathbf{c}) + r (\mathbf{c} \times \mathbf{a})
\]
for some scalars $p, q, \text{ and } r$, and $\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}) = 2$. Find $p + q + r$.

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