
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 the equation of circle $C$ as $x^{2}+y^{2}=4$.  
$(1)$ Find the equation of the line $l$ passing through point $P(2,1)$ and tangent to circle $C$.  
$(2)$ Let $M(x_{0},y_{0})$ be a moving point on circle $C$, and point $N$ has coordinates $(0,y_{0})$. If point $Q$ is the midpoint of $MN$, find the equation of the locus of point $Q$.

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