
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 $$\begin{cases} x=\cos\phi \\ y=\sin\phi \end{cases}$$ (where $\phi$ is the parameter), and the parametric equation of curve $C_2$ is $$\begin{cases} x=a\cos\phi \\ y=b\sin\phi \end{cases}$$ (where $a>b>0$, $\phi$ is the parameter). In the polar coordinate system with O as the pole and the positive x-axis as the polar axis, the ray $l: \theta=\alpha$ intersects $C_1$ and $C_2$ at one point each. When $\alpha=0$, the distance between these two points is 2, and when $\alpha= \frac{\pi}{2}$, these two points coincide.
(Ⅰ) Explain what curves $C_1$ and $C_2$ are, and find the values of $a$ and $b$;
(Ⅱ) Suppose when $\alpha= \frac{\pi}{4}$, the intersections of $l$ with $C_1$ and $C_2$ are $A_1$ and $B_1$ respectively, and when $\alpha=- \frac{\pi}{4}$, the intersections are $A_2$ and $B_2$ respectively. Find the polar equations of lines $A_1A_2$ and $B_1B_2$.

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