
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, there is a line $l$ defined by the parametric equations $\begin{cases} x=t \\ y= \sqrt{5}+2t \end{cases}$ (where $t$ is the parameter). Using the origin O as the pole and the positive half of the x-axis as the polar axis, a polar coordinate system is established. The polar equation of curve C is given by $\rho^2\cos2\theta+4=0$.
(Ⅰ) Write down the Cartesian coordinate equation of curve C;
(Ⅱ) Given point A(0, $\sqrt{5}$), 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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