
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
Given that $F_{1}(-c,0)$ and $F_{2}(c, 0)$ are the left and right foci of the ellipse $G$: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (0 < b < a < 3)$, and point $P(2, \sqrt{2})$ is a point on ellipse $G$ with $|PF_{1}|-|PF_{2}|=a$.

(1) Find the equation of ellipse $G$;

(2) If line $l$ intersects ellipse $G$ at points $A$ and $B$, and $\overrightarrow{OA} \perp \overrightarrow{OB}$, where $O$ is the coordinate origin, determine whether the distance from $O$ to line $l$ is a constant value. If it is, find that value; if not, explain why.

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