
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 the ellipse $C$: $\frac{x^{2}}{4}+y^{2}=1$, the line $l$ intersects the ellipse $C$ at points $A$ and $B$, and $\overrightarrow{OA} \cdot \overrightarrow{OB}=0$ (where $O$ is the origin of the coordinate system).

(1) Investigate whether the distance from point $O$ to line $AB$ is a constant value. If it is, calculate this value; if not, explain the reason.

(2) Find the minimum value of $|OA|\bullet |OB|$.

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