
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 $A \in \alpha$, $p \notin \alpha$, $\overrightarrow{PA}=(-\frac{\sqrt{3}}{2}, \frac{1}{2}, \sqrt{2})$, and a normal vector of the plane $\alpha$ is $\overrightarrow{n}=(0,-\frac{1}{2},-\sqrt{2})$, find the angle between the line $PA$ and the plane $\alpha$.

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