
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 vectors $\mathbf{u}, \mathbf{v}, \mathbf{w}$ satisfy $\|\mathbf{u}\| = 2$, $\|\mathbf{v}\| = 4$, $\|\mathbf{w}\| = 6$, and $\mathbf{u} \times (\mathbf{u} \times \mathbf{v}) = \mathbf{w}$. If $\phi$ is the angle between $\mathbf{u}$ and $\mathbf{v}$, find $\sin \phi$.

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