
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 curve $C_1$ is $\begin{cases} x=a\cos{\phi} \\ y=b\sin{\phi} \end{cases}$ ($a > b > 0$, $\phi$ is the parameter), in the polar coordinate system with $O$ as the pole and the positive direction of the $x$-axis as the polar axis, the curve $C_2$ is a circle whose center is on the polar axis and passes through the pole. It is known that the point $M(1, \frac{\sqrt{3}}{2})$ on curve $C_1$ corresponds to the parameter $\phi=\frac{\pi}{3}$, and the ray $\theta=\frac{\pi}{3}$ intersects curve $C_2$ at point $D(1, \frac{\pi}{3})$.
- (Ⅰ) Find the equations of curves $C_1$ and $C_2$;
- (Ⅱ) If points $A(\rho_1, \theta)$ and $B(\rho_2, \theta+\frac{\pi}{2})$ are on curve $C_1$, find the value of $\frac{1}{\rho_1^2} + \frac{1}{\rho_2^2}$.

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