
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 \(\mathbf{u}\) be a unit vector, \(\mathbf{v}\) a vector such that \(\|\mathbf{v}\| = 3\), and \(\mathbf{w}\) be another vector defined by the relations \(\mathbf{u} \times \mathbf{v} = \mathbf{w} + 2\mathbf{u}\) and \(\mathbf{w} \times \mathbf{u} = -\mathbf{v}\). Compute \(\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w})\).

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