
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
Given vectors $\mathbf{a}$, $\mathbf{b}$, and $\mathbf{c}$ where $\|\mathbf{a}\| = \|\mathbf{b}\| = 1$, $\|\mathbf{c}\| = 3$, and
\[
\mathbf{a} \times (\mathbf{a} \times \mathbf{b}) + 2\mathbf{c} = \mathbf{0}.
\]
If $\theta$ is the angle between $\mathbf{a}$ and $\mathbf{c}$, determine all possible values of $\theta$ in degrees.

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