
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 \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) be vectors 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 \( \mathbf{b}, \) then find \( \sin \theta. \)

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