
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 $\mathbf{u},$ $\mathbf{v},$ $\mathbf{w}$ be unit vectors such that
\[\mathbf{u} \times (\mathbf{v} \times \mathbf{w}) = \frac{2\mathbf{v} - \mathbf{w}}{3},\] and such that $\{\mathbf{u}, \mathbf{v}, \mathbf{w}\}$ is a linearly independent set.

Determine the angle between $\mathbf{u}$ and $\mathbf{v},$ in degrees.

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