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

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