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

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