
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 $\mathbf{x}$, $\mathbf{y}$, and $\mathbf{z}$ be three vectors satisfying $\|\mathbf{x}\| = 1$, $\mathbf{y} \cdot \mathbf{x} = \frac{1}{2}$, and $\mathbf{z} \cdot \mathbf{x} = 0$ such that
\[\mathbf{x} = s (\mathbf{y} \times \mathbf{z}) + t (\mathbf{z} \times \mathbf{x}) + u (\mathbf{x} \times \mathbf{y})\]
for some scalars $s$, $t$, and $u$. Given that $\mathbf{x} \cdot (\mathbf{y} \times \mathbf{z}) = 2$, find the value of $s + t + u$.

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