
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 $\|\mathbf{a}\| = 2$, $\|\mathbf{b}\| = 3$, $\|\mathbf{c}\| = 4$, and the relation 
\[\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = 3\mathbf{b} + 2\mathbf{c}\]
holds. Assume that $\{\mathbf{a}, \mathbf{b}, \mathbf{c}\}$ is a linearly independent set. Find the angle between $\mathbf{a}$ and $\mathbf{c}$ in degrees.

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