
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 an ellipse $C: \frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1 (a > b > 0)$ with an eccentricity of $\frac { \sqrt {3}}{2}$, the line $x-y+2b=0$ is tangent to the circle $x^{2}+y^{2}=2$ and intersects the $y$-axis at point $M$.  
$(1)$ Find the equation of the ellipse $C$;  
$(2)$ If a line $l$ passing through point $M$ intersects the ellipse at points $A$ and $B$, point $P$ is the midpoint of $AB$, and point $Q$ has coordinates $(- \frac {9}{10},0)$, find the equation of line $l$ when $PQ$ is perpendicular to $AB$.

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