
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 rectangular coordinate system, each point on the curve $C\_1$ has its x-coordinate kept unchanged while its y-coordinate is shortened to half of the original, resulting in a new curve $C\_2$. With the coordinate origin $O$ as the pole and the positive half of the x-axis as the polar axis, the polar coordinate equation of curve $C\_1$ is $ρ = 2$.
(I) Find the parametric equation of curve $C\_2$;
(II) Two lines, $l\_1$ and $l\_2$, are symmetrical about the y-axis, pass through the origin $O$, and intersect with curve $C\_2$ at points $A$, $C$ and $B$, $D$ respectively, with point $A$ located in the first quadrant. When the perimeter of quadrilateral $ABCD$ is at its maximum, find the standard form equation of line $l\_1$.

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