
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 vectors $\mathbf{a}, \mathbf{b}, \mathbf{c}$ be such that $\|\mathbf{a}\| = 2, \|\mathbf{b}\| = 3, \|\mathbf{c}\| = 4$, and
\[\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) + 2\mathbf{b} = \mathbf{0}.\]
Find the smallest possible angle between $\mathbf{b}$ and $\mathbf{c}$, in degrees.

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