
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 $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ be unit vectors such that the angle between $\mathbf{a}$ and $\mathbf{b}$ is $\beta,$ and the angle between $\mathbf{c}$ and $\mathbf{a} \times \mathbf{b}$ is also $\beta.$ If $\mathbf{b} \cdot (\mathbf{c} \times \mathbf{a}) = \frac{1}{2},$ find the smallest possible value of $\beta,$ in degrees.

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