
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 of curve $C\_1$ are given by $x=cos φ, y=sin φ$ and the parametric equations of curve $C\_2$ are given by $x=a cos φ, y=b sin φ (a > b > 0)$, where $φ$ is a parameter. In the polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the ray $l: θ=α$ intersects both $C\_1$ and $C\_2$ at one point each. When $α=0$, the distance between these two intersection points is $2$, and when $α= \frac {π}{2}$, these two intersection points coincide.
(I) Explain what kind of curves $C\_1$ and $C\_2$ are, and find the values of $a$ and $b$.
(II) Let the intersection points of $l$ with $C\_1$ and $C\_2$ be $A\_1$ and $B\_1$ respectively when $α= \frac {π}{4}$, and $A\_2$ and $B\_2$ respectively when $α=- \frac {π}{4}$. Calculate the area of the quadrilateral $A\_1A\_2B\_2B\_1$.

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