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

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