
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. Consider the equation:
\[\mathbf{b} = s (\mathbf{b} \times \mathbf{c}) + t (\mathbf{c} \times \mathbf{a}) + u (\mathbf{a} \times \mathbf{b})\]
for some scalars $s,$ $t,$ and $u,$ where $\mathbf{b} \cdot (\mathbf{c} \times \mathbf{a}) = 1.$ Find $s + t + u.$

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