
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 $\mathbf{p},$ $\mathbf{q},$ $\mathbf{r}$ be vectors such that $\|\mathbf{p}\| = 2,$ $\|\mathbf{q}\| = 4,$ $\|\mathbf{r}\| = 6,$ and
\[\mathbf{p} \times (\mathbf{p} \times \mathbf{q}) = \mathbf{r}.\]If $\phi$ is the angle between $\mathbf{p}$ and $\mathbf{q},$ then find $\sin \phi.$

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