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