
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
In the plane $xOy$, it is known that the ellipse $C$: $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ passes through the point $P(2,1)$, and its eccentricity $e= \dfrac { \sqrt {3}}{2}$.  
$(1)$ Find the equation of the ellipse $C$;  
$(2)$ The equation of line $l$ is $y=- \dfrac {1}{2}x+1$, line $l$ intersects ellipse $C$ at points $A$ and $B$, find the value of $|AB|$.

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