
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 \(\mathbf{u}, \mathbf{v},\) and \(\mathbf{w}\) be three mutually orthogonal unit vectors, such that
\[\mathbf{u} = s (\mathbf{u} \times \mathbf{v}) + t (\mathbf{v} \times \mathbf{w}) + u (\mathbf{w} \times \mathbf{u})\]
for some scalars \(s\), \(t\), and \(u\), and \(\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w}) = 1.\) Find \(s + t + u.\)

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