
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 line $l$ passes through the left focus $F$ of the ellipse $\frac{x^{2}}{2}+y^{2}=1$ and intersects ellipse $C$ at points $A$ and $B$, with $O$ being the coordinate origin and $OA$ perpendicular to $OB$, find the distance from point $O$ to line $AB$.

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