
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 circle $O: x^2+y^2=4$ and its intersection point with the positive y-axis is $M$, point $M$ moves clockwise along circle $O$ for an arc length of $\frac{\pi}{2}$ to reach point $N$. Let the angle with $ON$ as its terminal side be $\alpha$, calculate $\tan \alpha$.

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