
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 $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ satisfy $\|\mathbf{a}\| = \|\mathbf{b}\| = \sqrt{2},$ $\|\mathbf{c}\| = 3,$ and
\[\mathbf{a} \times (\mathbf{a} \times \mathbf{c}) + \mathbf{b} = \mathbf{0}.\] If $\theta$ is the angle between $\mathbf{a}$ and $\mathbf{c}$, find all possible values of $\theta$, in degrees.

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