
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
An ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ has two foci and one of its vertices form an isosceles right triangle. The chord formed by the intersection of the line $x+y=0$ and the circle with center at the right vertex of the ellipse $C$ and radius $2b$ has a length of $2 \sqrt {3}$.
(I) Find the standard equation of the ellipse $C$;
(II) Let line $l$ pass through the right focus $F_{2}$ of ellipse $C$ and intersect the ellipse at points $P$ and $Q$. If the parallelogram with adjacent sides $OP$ and $OQ$ is a rectangle, find the equation of line $l$ that satisfies this condition.

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