
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 \(\mathbf{a}, \mathbf{b},\) and \(\mathbf{c}\) be given such that \(\|\mathbf{a}\| = 2, \|\mathbf{b}\| = 7, \|\mathbf{c}\| = 4,\) and
\[
\mathbf{a} \times (\mathbf{a} \times \mathbf{b}) = \mathbf{c}.
\]
If \(\theta\) is the angle between \(\mathbf{a}\) and \(\mathbf{b},\) calculate \(\sin \theta.\)

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