
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 vectors $a = (2\cos\alpha, 2\sin\alpha)$, $b = (2\cos\beta, 2\sin\beta)$, and the line $2x\cos\alpha - 2y\sin\alpha + 1 = 0$ is tangent to the circle $(x - \cos\beta)^2 + (y + \sin\beta)^2 = 1$, then the angle between vectors $a$ and $b$ is \_\_\_\_\_\_\_\_.

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