
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 $\|\mathbf{a}\| = 3$, $\|\mathbf{b}\| = 4$, $\|\mathbf{c}\| = 5$, and
\[
\mathbf{b} \times (\mathbf{b} \times \mathbf{c}) + 2\mathbf{a} = \mathbf{0}.
\]
Find the angle between $\mathbf{b}$ and $\mathbf{c}$ in degrees.

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