
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 Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases} x=1+t\cos \alpha \\ y=t\sin \alpha \end{cases}$ ($t$ is the parameter, $0 \leqslant \alpha < \pi$). In the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the polar equation of curve $C$ is $\rho^{2}= \frac {2}{1+\sin ^{2}\theta }$.  
$(1)$ Find the Cartesian coordinate equation of curve $C$;  
$(2)$ Let the coordinates of point $M$ be $(1,0)$, and line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $\frac {1}{|MA|}+ \frac {1}{|MB|}$.

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