
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 line is given by $\begin{cases} x= \frac {1}{ \sqrt {5}}t \\ y= \sqrt {5}+ \frac {2}{ \sqrt {5}}t\end{cases}$ (where $t$ is a parameter). With the origin $O$ as the pole and the positive $x$-axis as the polar axis, the polar equation of curve $C$ is $\rho^{2}\cos 2\theta+4=0$.

(Ⅰ) Write the Cartesian coordinate equation of curve $C$;  
(Ⅱ) Given point $A(0, \sqrt {5})$, the line $l$ intersects curve $C$ at points $M$ and $N$. Find the value of $\frac {1}{|AM|}+ \frac {1}{|AN|}$;

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