
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 that in triangle $\triangle ABC$, $\angle A=120^{\circ}$, let $\alpha=\frac{\overrightarrow{BA}}{|\overrightarrow{BA}| \cos A}+\frac{\overrightarrow{BC}}{|\overrightarrow{BC}| \cos C}$ and $\beta=\frac{\overrightarrow{CA}}{|\overrightarrow{CA}| \cos A}+\frac{\overrightarrow{CB}}{|\overrightarrow{CB}| \cos B}$. Find the angle between vectors $\alpha$ and $\beta$.

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