
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
The vectors $\mathbf{u},$ $\mathbf{v},$ and $\mathbf{w}$ satisfy $\|\mathbf{u}\| = \|\mathbf{v}\| = 1,$ $\|\mathbf{w}\| = 3,$ and
\[\mathbf{u} \times (\mathbf{u} \times \mathbf{w}) + \mathbf{v} = \mathbf{0}.\]If $\phi$ is the angle between $\mathbf{u}$ and $\mathbf{w},$ then find all possible values of $\phi,$ in degrees.

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